Background Material. Lagrange's Equations of Motion of a Single Particle. Lagrange's Equations of Motion for a System of Particles. Conservative Systems. Dissipative Forces. General Treatment of Moments and Products of Inertia. Lagrangian Treatment of Rigid Body Dynamics. The Euler Method of Rigid Body Dynamics. Small Oscillations about Positions of Equilibrium. Small Oscillations about Steady Motion. Forces of Constraint. Driving Forces Required to Establish Known Motions. Effects of Earth's Figure and Daily Rotation on Dynamical Problems. Application of Lagrange's Equations to Electrical and Electromechanical Systems. Hamilton's Equations of Motion. Hamilton's Principle. Basic Equations of Dynamics in Vector and Tensor Notation. Appendix: Relations between Direction Cosines.