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  +
= Theoretical Mechanics =
−
= Information Retrieval =
  
−
* '''Course name''': Information Retrieval
 +
* '''Course name''': Theoretical Mechanics
−
* '''Code discipline''': XYZ
 +
* '''Code discipline''':
−
* '''Subject area''': Data Science; Computer systems organization; Information systems; Real-time systems; Information retrieval; World Wide Web
 +
* '''Subject area''': Mechanics; mathematical modeling and calculating of mechanical systems.
   
 
== Short Description ==
  
== Short Description ==
−
This course covers the following concepts: Indexing; Relevance; Ranking; Information retrieval; Query.
 +
This course covers the following concepts: Mechanics: Physical principles and methods for calculating kinematic, static and dynamic problems of mechanics.
   
 
== Prerequisites ==
  
== Prerequisites ==
   
 
=== Prerequisite subjects ===
  
=== Prerequisite subjects ===
  +
* CSE203 — Mathematical Analysis II: Linear algebra, vectors and matrices, partial derivatives.
−
* CSE204 — Analytic Geometry And Linear Algebra II: matrix multiplication, matrix decomposition (SVD, ALS) and approximation (matrix norm), sparse matrix, stability of solution (decomposition), vector spaces, metric spaces, manifold, eigenvector and eigenvalue.
  
  +
* CSE205 — Differential Equations: ODE.
−
* CSE113 — Philosophy I - (Discrete Math and Logic): graphs, trees, binary trees, balanced trees, metric (proximity) graphs, diameter, clique, path, shortest path.
  
−
* CSE206 — Probability And Statistics: probability, likelihood, conditional probability, Bayesian rule, stochastic matrix and properties. Analysis: DFT, [discrete] gradient.
  
   
 
=== Prerequisite topics ===
  
=== Prerequisite topics ===
Line 24: Line 23:
 
! Section !! Topics within the section
  
! Section !! Topics within the section
 
|-
  
|-
  +
| Kinematics ||
−
| Information retrieval basics ||
 
−
# Introduction to IR, major concepts.
 +
# Introduction to theoretical mechanics
  +
# Kinematics of a particle
−
# Crawling and Web.
  
  +
# Translatory and rotational motion of a rigid body
−
# Quality assessment.
  
  +
# Plane motion of a rigid body
  +
# Spherical motion of a rigid body
  +
# Motion of a free rigid body
  +
# Resultant motion
 
|-
  
|-
  +
| Statics ||
−
| Text processing and indexing ||
 
  +
# Basic concepts and principles of Statics
−
# Building inverted index for text documents. Boolean retrieval model.
  
  +
# Parallel forces and couples
−
# Language, tokenization, stemming, searching, scoring.
  
  +
# Equilibrium of a rigid body system in 2D
−
# Spellchecking and wildcard search.
  
  +
# Equilibrium of a rigid body system in 3D
−
# Suggest and query expansion.
  
  +
# Friction
−
# Language modelling. Topic modelling.
  
  +
# Center of gravity
 
|-
  
|-
  +
| Dynamics ||
−
| Vector model and vector indexing ||
 
  +
# Particle dynamics
−
# Vector model
  
  +
# Theorem of the motion of the center of mass of a system
−
# Machine learning for vector embedding
  
  +
# Theorem of the change in the linear momentum of a system
−
# Vector-based index structures
  
  +
# Theorem of the change in the angular momentum of a system
  +
# Some cases of rigid body motion.
  +
# D’Alambert’s principle
  +
# Mechanical work and power
  +
# Theorem of the change in the kinetic energy of a system
  +
# The theory of impact
  +
# Oscillations
 
|-
  
|-
  +
| Analytical mechanics ||
−
| Advanced topics. Media processing ||
 
  +
# Constraints and their classification
−
# Image and video processing, understanding and indexing
  
  +
# Generalized coordinates
−
# Content-based image retrieval
  
  +
# Generalized forces
−
# Audio retrieval
  
  +
# The D’Alembert-Lagrange’s principle
−
# Hum to search
  
  +
# The principle of virtual work
−
# Relevance feedback
  
  +
# The General Equation of dynamics
  +
# Lagrange’s equations
  +
# The Hamilton’s equations
 
|}
 
|}
 
== Intended Learning Outcomes (ILOs) ==
  
== Intended Learning Outcomes (ILOs) ==
   
 
=== What is the main purpose of this course? ===
  
=== What is the main purpose of this course? ===
  +
The purpose of the course is to give basic and advanced knowledge on theoretical mechanics. The course covers kinematics of a particle and a rigid body, statics of rigid bodies, particle dynamics, dynamics of a system, analytical mechanics. The objective of the course is to give knowledge and skills which can be used further for calculating of kinematics, statics and dynamics of mechanical parts of robots and studying advanced courses on robotics.
−
The course is designed to prepare students to understand background theories of information retrieval systems and introduce different information retrieval systems. The course will focus on the evaluation and analysis of such systems as well as how they are implemented. Throughout the course, students will be involved in discussions, readings, and assignments to experience real world systems. The technologies and algorithms covered in this class include machine learning, data mining, natural language processing, data indexing, and so on.
  
   
 
=== ILOs defined at three levels ===
  
=== ILOs defined at three levels ===
Line 57: Line 71:
 
==== Level 1: What concepts should a student know/remember/explain? ====
  
==== Level 1: What concepts should a student know/remember/explain? ====
 
By the end of the course, the students should be able to ...
  
By the end of the course, the students should be able to ...
  +
* Methods for describing the laws of motion of a particle and a solid,
−
* Terms and definitions used in area of information retrieval,
  
  +
* Methods for calculating the speeds and accelerations of points and bodies included in a mechanical system,
−
* Search engine and recommender system essential parts,
  
−
* Quality metrics of information retrieval systems,
 +
* Methods for studying the equilibrium of mechanical systems,
  +
* Methods for creating differential equations of motion of a particle and a solid,
−
* Contemporary approaches to semantic data analysis,
  
  +
* Methods for creating differential equations of motion of a mechanical system based on the classical approach,
−
* Indexing strategies.
  
  +
* Methods for creating differential equations of motion of a mechanical system based on methods of analytical mechanics.
   
 
==== Level 2: What basic practical skills should a student be able to perform? ====
  
==== Level 2: What basic practical skills should a student be able to perform? ====
 
By the end of the course, the students should be able to ...
  
By the end of the course, the students should be able to ...
  +
* How to draw up and use calculation schemes,
−
* Understand background theories behind information retrieval systems,
  
  +
* What calculation methods can be used to solve a specific problem,
−
* How to design a recommender system from scratch,
  
  +
* What calculation methods are appropriate to use when solving a specific problem,
−
* How to evaluate quality of a particular information retrieval system,
  
  +
* What limitations and errors are imposed by a specific method when solving a problem.
−
* Core ideas and system implementation and maintenance,
  
−
* How to identify and fix information retrieval system problems.
  
   
 
==== Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios? ====
  
==== Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios? ====
 
By the end of the course, the students should be able to ...
  
By the end of the course, the students should be able to ...
  +
* Analyze and explain mechanical phenomena based on the laws and theorems of theoretical mechanics,
−
* Build a recommender service from scratch,
  
  +
* Apply the basic laws and methods of theoretical mechanics to solving technical problems,
−
* Implement a proper index for an unstructured dataset,
  
  +
* Create mathematical models, evaluate their value and the relativity of their limits of application.
−
* Plan quality measures for a new recommender service,
  
−
* Run initial data analysis and problem evaluation for a business task, related to information retrieval.
 
 
== Grading ==
  
== Grading ==
   
Line 85: Line 98:
 
! Grade !! Range !! Description of performance
  
! Grade !! Range !! Description of performance
 
|-
  
|-
−
| A. Excellent || 84-100 || -
 +
| A. Excellent || 90-100 || -
 
|-
  
|-
−
| B. Good || 72-83 || -
 +
| B. Good || 75-89 || -
 
|-
  
|-
−
| C. Satisfactory || 60-71 || -
 +
| C. Satisfactory || 60-74 || -
 
|-
  
|-
 
| D. Poor || 0-59 || -
  
| D. Poor || 0-59 || -
Line 100: Line 113:
 
! Activity Type !! Percentage of the overall course grade
  
! Activity Type !! Percentage of the overall course grade
 
|-
  
|-
−
| Labs/seminar classes || 35
 +
| Labs/seminar classes || 10
 
|-
  
|-
−
| Interim performance assessment || 70
 +
| Interim performance assessment || 50
 
|-
  
|-
−
| Exams || 0
 +
| Exams || 40
 
|}
  
|}
   
Line 113: Line 126:
   
 
=== Open access resources ===
  
=== Open access resources ===
  +
* S. Targ Theoretical Mechanics. A short course, 1968
−
* Manning, Raghavan, Schütze, An Introduction to Information Retrieval, 2008, Cambridge University Press
  
  +
* D. Deleanu Theoretical mechanics. Theory and applications / Dumitru Deleanu – Constanta: Nautica, 2012
−
* Baeza-Yates, Ribeiro-Neto, Modern Information Retrieval, 2011, Addison-Wesley
  
  +
* Stephen T. Thornton and Jerry B. Marion Classical Dynamics of Particles and Systems. 5th edition, 2004
−
* Buttcher, Clarke, Cormack, Information Retrieval: Implementing and Evaluating Search Engines, 2010, MIT Press
  
  +
* Meshchersky I.V. Collection of Problems in Theoretical Mechanics 2014
−
* Course repository in github.
  
  +
* Prof . Dr. Ing. Vasile Szolga Theoretical Mechanics, 2010
  +
* S.M. Targ Kratki kurs teoreticheskoi mechaniki, 1986 - in Russian
  +
* A.I. Lurie Analiticheskaya mechanika, 1961 - in Russian
  +
* Sbornik kursovych rabot po teoreticheskoi mechanike. A.A.Yablonski, 2000 - in Russian
  +
* Meshchersky I.V. Sbornik zadach po teoreticheskoi mechanike, 1986 - in Russian
   
 
=== Closed access resources ===
  
=== Closed access resources ===
Line 130: Line 148:
 
|-
  
|-
 
! Learning Activities !! Section 1 !! Section 2 !! Section 3 !! Section 4
  
! Learning Activities !! Section 1 !! Section 2 !! Section 3 !! Section 4
−
|-
  
−
| Development of individual parts of software product code || 1 || 1 || 1 || 1
  
 
|-
  
|-
 
| Homework and group projects || 1 || 1 || 1 || 1
  
| Homework and group projects || 1 || 1 || 1 || 1
  +
|-
  +
| Midterm evaluation || 1 || 1 || 0 || 0
 
|-
  
|-
 
| Testing (written or computer based) || 1 || 1 || 1 || 1
  
| Testing (written or computer based) || 1 || 1 || 1 || 1
Line 147: Line 165:
 
! Activity Type !! Content !! Is Graded?
  
! Activity Type !! Content !! Is Graded?
 
|-
  
|-
  +
| Question || Calculate of the kinematic parameters of the particle according to the given laws of motion, it is required to determine: <br> particle trajectory, <br> particle velocity, <br> particle acceleration and its normal and tangential components, <br> radius of curvature of the trajectory. || 1
−
| Question || Enumerate limitations for web crawling. || 1
  
 
|-
  
|-
  +
| Question || Calculate of the kinematic parameters of the planar mechanism, determine: <br> velocity of specific points of the mechanism and angular velocity of the links of the mechanism using the method of instantaneous velocity centers, <br> velocity of specific points of the mechanism and angular velocity of the links of the mechanism using the analytical method, <br> acceleration of specific points of the mechanism and angular accelerations of the links of the mechanism. || 1
−
| Question || Propose a strategy for A/B testing. || 1
  
 
|-
  
|-
  +
| Question || Calculate of the kinematics of the complex motion of a point, determine: <br> transport, relative and absolute velocity of the point, <br> transport, relative, Coriolis and absolute acceleration of the point. || 1
−
| Question || Propose recommender quality metric. || 1
  
 
|-
  
|-
  +
| Question || Calculate of the kinematics of gears, determine the gear ratio, angular velocities and angular accelerations of links, velocities and accelerations of specific points of links for: <br> gearbox with fixed axles, <br> planetary gearbox with parallel axes, <br> planetary gearbox with intersecting axes. || 1
−
| Question || Implement DCG metric. || 1
  
 
|-
  
|-
  +
| Question || Make a synthesis of the laws of motion of a point and a solid, taking into account given conditions and restrictions. || 0
−
| Question || Discuss relevance metric. || 1
  
 
|-
  
|-
−
| Question || Crawl website with respect to robots.txt. || 1
 +
| Question || Do a kinematic analysis of complex planar mechanisms with a large number of links. || 0
 
|-
  
|-
−
| Question || What is typical IR system architecture? || 0
 +
| Question || Do a kinematic analysis of complex planar mechanisms with several degrees of freedom. || 0
 
|-
  
|-
−
| Question || Show how to parse a dynamic web page. || 0
 +
| Question || Do a kinematic analysis of spatial mechanisms. || 0
 
|-
  
|-
−
| Question || Provide a framework to accept/reject A/B testing results. || 0
 +
| Question || Do a kinematic analysis of the complex motion of a solid body. || 0
−
|-
  
−
| Question || Compute DCG for an example query for random search engine. || 0
  
−
|-
  
−
| Question || Implement a metric for a recommender system. || 0
  
−
|-
  
−
| Question || Implement pFound. || 0
  
 
|}
 
|}
 
==== Section 2 ====
  
==== Section 2 ====
Line 177: Line 189:
 
! Activity Type !! Content !! Is Graded?
  
! Activity Type !! Content !! Is Graded?
 
|-
  
|-
−
| Question || Build inverted index for a text. || 1
 +
| Question || Derive equilibrium equations for a system of concurrent forces. || 1
 
|-
  
|-
−
| Question || Tokenize a text. || 1
 +
| Question || Derive equilibrium equations for a solid in 2D. || 1
 
|-
  
|-
−
| Question || Implement simple spellchecker. || 1
 +
| Question || Derive equilibrium equations for a system of two or more solids in 2D. || 1
 
|-
  
|-
−
| Question || Implement wildcard search. || 1
 +
| Question || Derive equilibrium equations for a solid in 3D. || 1
 
|-
  
|-
−
| Question || Build inverted index for a set of web pages. || 0
 +
| Question || Apply equilibrium equations to calculate the reactions of supports and forces in the rods of a truss in 2D. || 0
 
|-
  
|-
−
| Question || build a distribution of stems/lexemes for a text. || 0
 +
| Question || Apply equilibrium equations to calculate the reactions of supports of a solid body in 2D. || 0
 
|-
  
|-
−
| Question || Choose and implement case-insensitive index for a given text collection. || 0
 +
| Question || Apply equilibrium equations for calculating the reactions of supports of a system of bodies in 2D. || 0
 
|-
  
|-
−
| Question || Choose and implement semantic vector-based index for a given text collection. || 0
 +
| Question || Apply equilibrium equations to calculate the reactions of supports of a solid body in 3D. || 0
  +
|-
  +
| Question || Investigate the equilibrium of a system of bodies taking into account friction. || 0
 
|}
 
|}
 
==== Section 3 ====
  
==== Section 3 ====
Line 199: Line 213:
 
! Activity Type !! Content !! Is Graded?
  
! Activity Type !! Content !! Is Graded?
 
|-
  
|-
−
| Question || Embed the text with an ML model. || 1
 +
| Question || Derive and solve the differential equations of rectilinear and curvilinear motion of a particle. || 1
 
|-
  
|-
  +
| Question || Derive and solve differential equations based on the theorem on the motion of the center of mass of a system. || 1
−
| Question || Build term-document matrix. || 1
  
 
|-
  
|-
  +
| Question || Derive and solve differential equations based on the theorem on the change in the angular momentum of a system. || 1
−
| Question || Build semantic index for a dataset using Annoy. || 1
  
 
|-
  
|-
  +
| Question || Derive and solve the differential equations of rectilinear and curvilinear motion of bodies that form a system with one degree of freedom. || 1
−
| Question || Build kd-tree index for a given dataset. || 1
  
 
|-
  
|-
  +
| Question || Derive and solve differential equations of motion based on the D’Alembert’s principle. || 1
−
| Question || Why kd-trees work badly in 100-dimensional environment? || 1
  
 
|-
  
|-
−
| Question || What is the difference between metric space and vector space? || 1
 +
| Question || Derive and solve the differential equation based on the theorem on the change in kinetic energy. || 1
 
|-
  
|-
  +
| Question || Apply the differential equations of a particle to study the motion of a body in a field of gravity under the influence of air resistance. || 0
−
| Question || Choose and implement persistent index for a given text collection. || 0
  
 
|-
  
|-
−
| Question || Visualize a dataset for text classification. || 0
 +
| Question || Apply the differential equations of a particle to study oscillations. || 0
 
|-
  
|-
  +
| Question || Apply the theorem on the motion of the center of mass of a system to determine the dynamic reactions of the support of the mechanism. || 0
−
| Question || Build (H)NSW index for a dataset. || 0
  
 
|-
  
|-
−
| Question || Compare HNSW to Annoy index. || 0
 +
| Question || Apply the theorem on the change in the angular momentum of a system to study the gyroscopic effect. || 0
 
|-
  
|-
  +
| Question || Apply the D’Alembert’s principle to determine the dynamic reactions of the supports of a mechanical system || 0
−
| Question || What are metric space index structures you know? || 0
  
  +
|-
  +
| Question || Apply the kinetic energy change theorem to determine the velosity of bodies of a mechanical system. || 0
 
|}
 
|}
 
==== Section 4 ====
  
==== Section 4 ====
Line 227: Line 243:
 
! Activity Type !! Content !! Is Graded?
  
! Activity Type !! Content !! Is Graded?
 
|-
  
|-
−
| Question || Extract semantic information from images. || 1
 +
| Question || What are generalized coordinates? || 1
  +
|-
  +
| Question || What are cyclic coordinates? || 1
 
|-
  
|-
  +
| Question || Derive the differential equations of a mechanical system based on the principle of virtual work || 1
−
| Question || Build an image hash. || 1
  
 
|-
  
|-
−
| Question || Build a spectral representation of a song. || 1
 +
| Question || Derive the differential equations of a mechanical system based on the General Equation of dynamics || 1
 
|-
  
|-
−
| Question || Whats is relevance feedback? || 1
 +
| Question || Derive the differential equations of a mechanical system based on Lagrange’s equations || 1
 
|-
  
|-
  +
| Question || Apply the principle of virtual work to study the laws of motion of a mechanical system with one degree of freedom. || 0
−
| Question || Build a "search by color" feature. || 0
  
 
|-
  
|-
  +
| Question || Apply the General Equation of dynamics to study the laws of motion of a mechanical system with one degree of freedom. || 0
−
| Question || Extract scenes from video. || 0
  
 
|-
  
|-
  +
| Question || Apply the Lagrange’s equations to study the laws of motion of a mechanical system with several degrees of freedom. || 0
−
| Question || Write a voice-controlled search. || 0
  
 
|-
  
|-
  +
| Question || Apply the Lagrange’s equations to study the oscillations of a mechanical system with two degrees of freedom. || 0
−
| Question || Semantic search within unlabelled image dataset. || 0
  
 
|}
 
|}
 
=== Final assessment ===
  
=== Final assessment ===
 
'''Section 1'''
  
'''Section 1'''
  +
# Describe the vector, coordinate, and natural methods of specifying particle motion. Show the transition from one method to another. Find the velocity and acceleration of the particle in various methods.
−
# Implement text crawler for a news site.
  
  +
# Define the angular velocity vector and the angular acceleration vector of the body. Prove the independence of these vectors from the choice of the pole. Use the Euler vector formula to find the velocities and accelerations of points of a rotating rigid body and a rigid body making plane motion.
−
# What is SBS (side-by-side) and how is it used in search engines?
  
  +
# Describe ways to set the orientation of a solid in space, including Euler angles, Tight-Brian angles, quaternions. Show the methodology for determining the angular velocity vector in these cases.
−
# Compare pFound with CTR and with DCG.
  
  +
# Show the methodology of kinematic analysis of planar mechanisms, including the method of composing the equations of motion for the points of the mechanism, the theorems on the velocities and accelerations of body points in plane motion, and the instantaneous center of velocity method.
−
# Explain how A/B testing works.
  
  +
# Show the methodology of kinematic analysis of the complex motion of a particle, the theorems on the addition of velocities and accelerations for complex motion of a particle.
−
# Describe PageRank algorithm.
  
 
'''Section 2'''
  
'''Section 2'''
−
# Explain how (and why) KD-trees work.
 +
# Explain the basic axioms of statics.
  +
# Demonstrate the methods for determining the moment of force about a point and about an axis.
−
# What are weak places of inverted index?
  
  +
# Demonstrate the methods for transformation a couple of forces.
−
# Compare different text vectorization approaches.
  
  +
# Demonstrate the method for determining the principal vector and the principal moment of the force system.
−
# Compare tolerant retrieval to spellchecking.
  
  +
# Describe the method for transformation a force system to the simplest possible form.
 
'''Section 3'''
  
'''Section 3'''
  +
# Formulate the theorem of the motion of the center of mass of a system. Show for what problems this theorem is effective.
−
# Compare inverted index to HNSW in terms of speed, memory consumption?
  
  +
# Formulate the D’Alambert’s principle. Show for what problems the calculation method based on this principle is effective.
−
# Choose the best index for a given dataset.
  
  +
# Describe the concept of force field. Show the method for determining the work of a force at a movement of a particle in a potential force field.
−
# Implement range search in KD-tree.
  
  +
# Describe the processes that occur upon impact and methods for calculating the law of motion of the body upon impact.
 
'''Section 4'''
  
'''Section 4'''
  +
# Formulate the the principle of virtual work. Show for what problems the calculation method based on this principle is effective.
−
# What are the approaches to image understanding?
  
  +
# Formulate the the D’Alembert-Lagrange’s principle. Show for problems tasks the calculation method based on this principle is effective.
−
# How to cluster a video into scenes and shots?
  
  +
# Demonstrate methods for calculating generalized forces.
−
# How speech-to-text technology works?
  
  +
# Show the different forms of writing the Lagrange equations and explain in which cases each of these forms will be more convenient.
−
# How to build audio fingerprints?
  
  +
# Demonstrate the principles of choosing the most convenient method for solving a given specific problem of mechanics.
   
 
=== The retake exam ===
  
=== The retake exam ===

Revision as of 13:22, 10 November 2022

Theoretical Mechanics

  • Course name: Theoretical Mechanics
  • Code discipline:
  • Subject area: Mechanics; mathematical modeling and calculating of mechanical systems.

Short Description

This course covers the following concepts: Mechanics: Physical principles and methods for calculating kinematic, static and dynamic problems of mechanics.

Prerequisites

Prerequisite subjects

  • CSE203 — Mathematical Analysis II: Linear algebra, vectors and matrices, partial derivatives.
  • CSE205 — Differential Equations: ODE.

Prerequisite topics

Course Topics

Course Sections and Topics
Section Topics within the section
Kinematics
  1. Introduction to theoretical mechanics
  2. Kinematics of a particle
  3. Translatory and rotational motion of a rigid body
  4. Plane motion of a rigid body
  5. Spherical motion of a rigid body
  6. Motion of a free rigid body
  7. Resultant motion
Statics
  1. Basic concepts and principles of Statics
  2. Parallel forces and couples
  3. Equilibrium of a rigid body system in 2D
  4. Equilibrium of a rigid body system in 3D
  5. Friction
  6. Center of gravity
Dynamics
  1. Particle dynamics
  2. Theorem of the motion of the center of mass of a system
  3. Theorem of the change in the linear momentum of a system
  4. Theorem of the change in the angular momentum of a system
  5. Some cases of rigid body motion.
  6. D’Alambert’s principle
  7. Mechanical work and power
  8. Theorem of the change in the kinetic energy of a system
  9. The theory of impact
  10. Oscillations
Analytical mechanics
  1. Constraints and their classification
  2. Generalized coordinates
  3. Generalized forces
  4. The D’Alembert-Lagrange’s principle
  5. The principle of virtual work
  6. The General Equation of dynamics
  7. Lagrange’s equations
  8. The Hamilton’s equations

Intended Learning Outcomes (ILOs)

What is the main purpose of this course?

The purpose of the course is to give basic and advanced knowledge on theoretical mechanics. The course covers kinematics of a particle and a rigid body, statics of rigid bodies, particle dynamics, dynamics of a system, analytical mechanics. The objective of the course is to give knowledge and skills which can be used further for calculating of kinematics, statics and dynamics of mechanical parts of robots and studying advanced courses on robotics.

ILOs defined at three levels

Level 1: What concepts should a student know/remember/explain?

By the end of the course, the students should be able to ...

  • Methods for describing the laws of motion of a particle and a solid,
  • Methods for calculating the speeds and accelerations of points and bodies included in a mechanical system,
  • Methods for studying the equilibrium of mechanical systems,
  • Methods for creating differential equations of motion of a particle and a solid,
  • Methods for creating differential equations of motion of a mechanical system based on the classical approach,
  • Methods for creating differential equations of motion of a mechanical system based on methods of analytical mechanics.

Level 2: What basic practical skills should a student be able to perform?

By the end of the course, the students should be able to ...

  • How to draw up and use calculation schemes,
  • What calculation methods can be used to solve a specific problem,
  • What calculation methods are appropriate to use when solving a specific problem,
  • What limitations and errors are imposed by a specific method when solving a problem.

Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?

By the end of the course, the students should be able to ...

  • Analyze and explain mechanical phenomena based on the laws and theorems of theoretical mechanics,
  • Apply the basic laws and methods of theoretical mechanics to solving technical problems,
  • Create mathematical models, evaluate their value and the relativity of their limits of application.

Grading

Course grading range

Grade Range Description of performance
A. Excellent 90-100 -
B. Good 75-89 -
C. Satisfactory 60-74 -
D. Poor 0-59 -

Course activities and grading breakdown

Activity Type Percentage of the overall course grade
Labs/seminar classes 10
Interim performance assessment 50
Exams 40

Recommendations for students on how to succeed in the course

Resources, literature and reference materials

Open access resources

  • S. Targ Theoretical Mechanics. A short course, 1968
  • D. Deleanu Theoretical mechanics. Theory and applications / Dumitru Deleanu – Constanta: Nautica, 2012
  • Stephen T. Thornton and Jerry B. Marion Classical Dynamics of Particles and Systems. 5th edition, 2004
  • Meshchersky I.V. Collection of Problems in Theoretical Mechanics 2014
  • Prof . Dr. Ing. Vasile Szolga Theoretical Mechanics, 2010
  • S.M. Targ Kratki kurs teoreticheskoi mechaniki, 1986 - in Russian
  • A.I. Lurie Analiticheskaya mechanika, 1961 - in Russian
  • Sbornik kursovych rabot po teoreticheskoi mechanike. A.A.Yablonski, 2000 - in Russian
  • Meshchersky I.V. Sbornik zadach po teoreticheskoi mechanike, 1986 - in Russian

Closed access resources

Software and tools used within the course

Teaching Methodology: Methods, techniques, & activities

Activities and Teaching Methods

Activities within each section
Learning Activities Section 1 Section 2 Section 3 Section 4
Homework and group projects 1 1 1 1
Midterm evaluation 1 1 0 0
Testing (written or computer based) 1 1 1 1

Formative Assessment and Course Activities

Ongoing performance assessment

Section 1

Activity Type Content Is Graded?
Question Calculate of the kinematic parameters of the particle according to the given laws of motion, it is required to determine:
particle trajectory,
particle velocity,
particle acceleration and its normal and tangential components,
radius of curvature of the trajectory.		 1
Question Calculate of the kinematic parameters of the planar mechanism, determine:
velocity of specific points of the mechanism and angular velocity of the links of the mechanism using the method of instantaneous velocity centers,
velocity of specific points of the mechanism and angular velocity of the links of the mechanism using the analytical method,
acceleration of specific points of the mechanism and angular accelerations of the links of the mechanism.		 1
Question Calculate of the kinematics of the complex motion of a point, determine:
transport, relative and absolute velocity of the point,
transport, relative, Coriolis and absolute acceleration of the point.		 1
Question Calculate of the kinematics of gears, determine the gear ratio, angular velocities and angular accelerations of links, velocities and accelerations of specific points of links for:
gearbox with fixed axles,
planetary gearbox with parallel axes,
planetary gearbox with intersecting axes.		 1
Question Make a synthesis of the laws of motion of a point and a solid, taking into account given conditions and restrictions. 0
Question Do a kinematic analysis of complex planar mechanisms with a large number of links. 0
Question Do a kinematic analysis of complex planar mechanisms with several degrees of freedom. 0
Question Do a kinematic analysis of spatial mechanisms. 0
Question Do a kinematic analysis of the complex motion of a solid body. 0

Section 2

Activity Type Content Is Graded?
Question Derive equilibrium equations for a system of concurrent forces. 1
Question Derive equilibrium equations for a solid in 2D. 1
Question Derive equilibrium equations for a system of two or more solids in 2D. 1
Question Derive equilibrium equations for a solid in 3D. 1
Question Apply equilibrium equations to calculate the reactions of supports and forces in the rods of a truss in 2D. 0
Question Apply equilibrium equations to calculate the reactions of supports of a solid body in 2D. 0
Question Apply equilibrium equations for calculating the reactions of supports of a system of bodies in 2D. 0
Question Apply equilibrium equations to calculate the reactions of supports of a solid body in 3D. 0
Question Investigate the equilibrium of a system of bodies taking into account friction. 0

Section 3

Activity Type Content Is Graded?
Question Derive and solve the differential equations of rectilinear and curvilinear motion of a particle. 1
Question Derive and solve differential equations based on the theorem on the motion of the center of mass of a system. 1
Question Derive and solve differential equations based on the theorem on the change in the angular momentum of a system. 1
Question Derive and solve the differential equations of rectilinear and curvilinear motion of bodies that form a system with one degree of freedom. 1
Question Derive and solve differential equations of motion based on the D’Alembert’s principle. 1
Question Derive and solve the differential equation based on the theorem on the change in kinetic energy. 1
Question Apply the differential equations of a particle to study the motion of a body in a field of gravity under the influence of air resistance. 0
Question Apply the differential equations of a particle to study oscillations. 0
Question Apply the theorem on the motion of the center of mass of a system to determine the dynamic reactions of the support of the mechanism. 0
Question Apply the theorem on the change in the angular momentum of a system to study the gyroscopic effect. 0
Question Apply the D’Alembert’s principle to determine the dynamic reactions of the supports of a mechanical system 0
Question Apply the kinetic energy change theorem to determine the velosity of bodies of a mechanical system. 0

Section 4

Activity Type Content Is Graded?
Question What are generalized coordinates? 1
Question What are cyclic coordinates? 1
Question Derive the differential equations of a mechanical system based on the principle of virtual work 1
Question Derive the differential equations of a mechanical system based on the General Equation of dynamics 1
Question Derive the differential equations of a mechanical system based on Lagrange’s equations 1
Question Apply the principle of virtual work to study the laws of motion of a mechanical system with one degree of freedom. 0
Question Apply the General Equation of dynamics to study the laws of motion of a mechanical system with one degree of freedom. 0
Question Apply the Lagrange’s equations to study the laws of motion of a mechanical system with several degrees of freedom. 0
Question Apply the Lagrange’s equations to study the oscillations of a mechanical system with two degrees of freedom. 0

Final assessment

Section 1

  1. Describe the vector, coordinate, and natural methods of specifying particle motion. Show the transition from one method to another. Find the velocity and acceleration of the particle in various methods.
  2. Define the angular velocity vector and the angular acceleration vector of the body. Prove the independence of these vectors from the choice of the pole. Use the Euler vector formula to find the velocities and accelerations of points of a rotating rigid body and a rigid body making plane motion.
  3. Describe ways to set the orientation of a solid in space, including Euler angles, Tight-Brian angles, quaternions. Show the methodology for determining the angular velocity vector in these cases.
  4. Show the methodology of kinematic analysis of planar mechanisms, including the method of composing the equations of motion for the points of the mechanism, the theorems on the velocities and accelerations of body points in plane motion, and the instantaneous center of velocity method.
  5. Show the methodology of kinematic analysis of the complex motion of a particle, the theorems on the addition of velocities and accelerations for complex motion of a particle.

Section 2

  1. Explain the basic axioms of statics.
  2. Demonstrate the methods for determining the moment of force about a point and about an axis.
  3. Demonstrate the methods for transformation a couple of forces.
  4. Demonstrate the method for determining the principal vector and the principal moment of the force system.
  5. Describe the method for transformation a force system to the simplest possible form.

Section 3

  1. Formulate the theorem of the motion of the center of mass of a system. Show for what problems this theorem is effective.
  2. Formulate the D’Alambert’s principle. Show for what problems the calculation method based on this principle is effective.
  3. Describe the concept of force field. Show the method for determining the work of a force at a movement of a particle in a potential force field.
  4. Describe the processes that occur upon impact and methods for calculating the law of motion of the body upon impact.

Section 4

  1. Formulate the the principle of virtual work. Show for what problems the calculation method based on this principle is effective.
  2. Formulate the the D’Alembert-Lagrange’s principle. Show for problems tasks the calculation method based on this principle is effective.
  3. Demonstrate methods for calculating generalized forces.
  4. Show the different forms of writing the Lagrange equations and explain in which cases each of these forms will be more convenient.
  5. Demonstrate the principles of choosing the most convenient method for solving a given specific problem of mechanics.

The retake exam

Section 1

Section 2

Section 3

Section 4

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