Dynamics

Calendar

LEC #	TOPICS	KEY DATES
1	Course Overview Single Particle Dynamics: Linear and Angular Momentum Principles, Work-energy Principle
2	Examples of Single Particle Dynamics
3	Examples of Single Particle Dynamics (cont.)
4	Dynamics of Systems of Particles: Linear and Angular Momentum Principles, Work-energy Principle
5	Dynamics of Systems of Particles (cont.): Examples Rigid Bodies: Degrees of Freedom	Problem set 1 due
6	Translation and Rotation of Rigid Bodies Existence of Angular Velocity Vector
7	Linear Superposition of Angular Velocities Angular Velocity in 2D Differentiation in Rotating Frames	Problem set 2 due
8	Linear and Angular Momentum Principle for Rigid Bodies
9	Work-energy Principle for Rigid Bodies	Problem set 3 due
10	Examples for Lecture 8 Topics
11	Examples for Lecture 9 Topics	Problem set 4 due
12	Gyroscopes: Euler Angles, Spinning Top, Poinsot Plane, Energy Ellipsoid Linear Stability of Stationary Gyroscope Motion
13	Generalized Coordinates, Constraints, Virtual Displacements	Problem set 5 due
14	Exam 1
15	Generalized Coordinates, Constraints, Virtual Displacements (cont.)
16	Virtual Work, Generalized Force, Conservative Forces Examples
17	D’Alembert’s Principle Extended Hamilton’s Principle Principle of Least Action	Problem set 6 due
18	Examples for Lecture 16 Topics Lagrange’s Equation of Motion
19	Examples for Lecture 17 Topics	Problem set 7 due
20	Lagrange Multipliers, Determining Holonomic Constraint Forces, Lagrange’s Equation for Nonholonomic Systems, Examples	Problem set 8 due
21	Stability of Conservative Systems Dirichlet’s Theorem Example
22	Linearized Equations of Motion Near Equilibria of Holonomic Systems	Problem set 9 due
23	Linearized Equations of Motion for Conservative Systems Stability Normal Modes Mode Shapes Natural Frequencies
24	Examples for Lecture 23 Topics Orthogonality of Modes Shapes Principal Coordinates	Problem set 10 due
25	Damped and Forced Vibrations Near Equilibria
26	Exam 2