Course information

Kinematics: Translation and Rotation, Rotation about a Fixed Axis – General Motion, Instantaneous Center of Rotation in Plane Motion. Absolute and Relative Velocity and Acceleration, Rate of Change of a Vector with Respect to a Rotating Frame. Motion of a Particle Relative to a Rotating Frame, Coriolis Acceleration. Three-Dimensional Motion of a Particle Relative to a Rotating Frame. Vector Dynamics: Plane Motion of Rigid Bodies: Forces and Accelerations, Equations of Motion for a Rigid Body, Angular Momentum in Plane Motion. Plane Motion of Rigid Bodies: Energy and Momentum Methods, Principle of Work and Energy for a Rigid Body, Work of Forces Acting on a Rigid Body, Kinetic Energy of a Rigid Body in Plane Motion, Systems of Rigid Bodies, Conservation of Energy. Principle of Impulse and Momentum for the Plane Motion of a Rigid Body, Systems of Rigid Bodies, Conservation of Angular Momentum. Kinetics of Rigid Bodies in Three Dimensions: Angular Momentum of a Rigid Body, Application of the Principle of Impulse and Momentum, Kinetic Energy, Euler’s Equations of Motion. Analytical Dynamics: Lagrangian dynamics: Principle of virtual work, D’Alembert’s principle, Holonomic and non-holonomic constraints, forces of constraints, generalized coordinates, Lagrange’s equations of motion. Generalized momenta - ignorable coordinates - conservation theorems, generalized energy – Jacobi’s integral, position-velocity space, motion of charged particles in electromagnetic fields – Lorentz’s force, symmetries and invariants, Noether’s theorem. Variational principles: Advantages of variational formulations, Hamilton’s principle, calculus of variations and Euler-Lagrange equations, extension to non-holonomic systems, constraint forces and Lagrange multipliers. Hamiltonian dynamics: Canonical variables and phase space, Canonical equations of motion, Legendre’s transformation, symplectic description, derivation of the canonical equations from a variational principle, autonomous and non-autonomous systems, Liouville’s theorem.