1 1. History of Dynamics; Motion in Moving Reference Frames 2 2. Newton's Laws & Describing the Kinematics of Particles 3 3. Motion of Center of Mass; Acceleration in Rotating Ref. Frames 4 4. Movement of a Particle in Circular Motion w/ Polar Coordinates 5 R2. Velocity and Acceleration in Translating and Rotating Frames 6 5. Impulse, Torque, & Angular Momentum for a System of Particles 7 6. Torque & the Time Rate of Change of Angular Momentum 8 R3. Motion in Moving Reference Frames 9 7. Degrees of Freedom, Free Body Diagrams, & Fictitious Forces 10 8. Fictitious Forces & Rotating Mass 11 R4. Free Body Diagrams 12 9. Rotating Imbalance 13 10. Equations of Motion, Torque, Angular Momentum of Rigid Bodies 14 R5. Equations of Motion 15 11. Mass Moment of Inertia of Rigid Bodies 16 12. Problem Solving Methods for Rotating Rigid Bodies 17 R6. Angular Momentum and Torque 18 13. Four Classes of Problems With Rotational Motion 19 14. More Complex Rotational Problems & Their Equations of Motion 20 R7. Cart and Pendulum, Direct Method 21 Notation Systems 22 15. Introduction to Lagrange With Examples 23 R8. Cart and Pendulum, Lagrange Method 24 16. Kinematic Approach to Finding Generalized Forces 25 17. Practice Finding EOM Using Lagrange Equations 26 R9. Generalized Forces 27 18. Quiz Review From Optional Problem Set 8 28 19. Introduction to Mechanical Vibration 29 20. Linear System Modeling a Single Degree of Freedom Oscillator 30 21. Vibration Isolation 31 22. Finding Natural Frequencies & Mode Shapes of a 2 DOF System 32 R10. Steady State Dynamics 33 23. Vibration by Mode Superposition 34 24. Modal Analysis: Orthogonality, Mass Stiffness, Damping Matrix 35 R11. Double Pendulum System 36 25. Modal Analysis: Response to IC's and to Harmonic Forces 37 26. Response of 2-DOF Systems by the Use of Transfer Functions 38 27. Vibration of Continuous Structures: Strings, Beams, Rods, etc. 39 R12. Modal Analysis of a Double Pendulum System