ME502 ADVANCED DYNAMICS
| Course Code: | 5690502 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mechanical Engineering |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. MUSTAFA KEMAL ÖZGÖREN |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
This course aims to train the students in the following topics of kinematics and dynamics of spatial systems.
1. Particle kinematics: Rectangular, cylindrical, and spherical coordinates.
2. Path frame description of motion: Tangential and normal accelerations. Center and radius of curvature. Torsion. Curve-tracking and torsional angular velocities.
3. Vectors and Dyadics. Rotation of a vector and rotation dyadic.
4. Matrix representation of vectors and dyadics in different reference frames. Component transformation matrices.
5. Vector differentiation with respect to different reference frames. Coriolis-Transport theorem. Relative angular velocities and accelerations.
6. Velocity and acceleration of a point with respect to different reference frames.
7. Newtonian mechanics for a particle: Three laws of Newton. Force-acceleration, impulse-momentum, and work-energy relationships.
8. Newtonian mechanics for a system of particles: Force-acceleration, impulse-momentum, and work-energy relationships.
9. Conservative forces and potential energy.
10. Newtonian mechanics for a rigid body.
11. Newtonian mechanics for a system of rigid bodies. Interaction forces and moments.
12. Dynamic analysis via work-energy methods. Virtual work method based on d'Alembert's principle. Hamilton's principle.
13. Lagrange's equations without constraints.
14. Lagrange's equations with holonomic and nonholonomic constraints. Lagrange multipliers and constraint forces.
Course Content
Three dimensional kinematics: Coordinate systems and transformation. Spatial rotations. Euler angles. Relative velocity and acceleration relationships. Basics of Newtonian mechanics. Inertia tensor. Rigid body dynamics. Gyroscopic effects. Analytical mechanics: Hamilton's principle. Generalized coordinates and forces. Lagrange's equations. Holonomic and nonholonomic constraints. Lagrange multipliers and Lagrange's equations with constraints. Hamilton's equations. (F)
Course Learning Outcomes
A student who passes this course successfully will acquire the following qualities.
1. Expediency in analyzing spatial motions of particles.
2. Expediency in the path frame motion analysis of a particle and familiarity with the concepts of curvature and torsion.
3. Expediency in working with vectors, dyadics, and rotation dyadics in particular.
4. Expediency in the matrix representation of vectors and dyadics in different reference frames and the component transformation matrices.
5. Expediency in vector differentiation with respect to different reference frames and the relevant angular velocities and accelerations.
6. Expediency in using relative velocities and accelerations of a point with respect to different reference frames.
7. Expediency in using Newtonian mechanics for a particle and a system of particles.
8. Expediency in using the force-acceleration, impulse-momentum, and work-energy relationships.
9. Familiarity with conservative forces and potential energy.
10. Expediency in using Newtonian mechanics for a rigid body and familiarity with the gyroscopic effects.
11. Expediency in studying interacting rigid bodies together with the interaction forces and moments.
12. Expediency in using the Lagrange's equations without constraints.
13. Expediency in using Lagrange's equations with holonomic and nonholonomic constraints together with the constraint forces.