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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
| Section | Topics within the section |
|---|---|
| Kinematics |
|
| Statics |
|
| Dynamics |
|
| Analytical mechanics |
|
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
| 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
- 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.
- 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.
- 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.
- 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.
- 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
- Explain the basic axioms of statics.
- Demonstrate the methods for determining the moment of force about a point and about an axis.
- Demonstrate the methods for transformation a couple of forces.
- Demonstrate the method for determining the principal vector and the principal moment of the force system.
- Describe the method for transformation a force system to the simplest possible form.
Section 3
- Formulate the theorem of the motion of the center of mass of a system. Show for what problems this theorem is effective.
- Formulate the D’Alambert’s principle. Show for what problems the calculation method based on this principle is effective.
- 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.
- Describe the processes that occur upon impact and methods for calculating the law of motion of the body upon impact.
Section 4
- Formulate the the principle of virtual work. Show for what problems the calculation method based on this principle is effective.
- Formulate the the D’Alembert-Lagrange’s principle. Show for problems tasks the calculation method based on this principle is effective.
- Demonstrate methods for calculating generalized forces.
- Show the different forms of writing the Lagrange equations and explain in which cases each of these forms will be more convenient.
- 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