Spatial dynamical equations of Euler for the rigid body, properties of the inertia tensor, principal axes, dynamical equations of the rotating top, solution for the moment-free rotation, nutation, stability of rotations about principal axes, solution for the constant moment, precession.
Lagrange equations of the first kind, notation for vector functions of vectors and their partial derivatives, types of constraints, degrees of freedom, Jacobian of constraint equations, virtual displacements, D’Alembert’s principle of orthogonality of constraint forces, Lagrange Multipliers, geometrical interpretation of the effect of Lagrange-Multipliers, solution strategies for the Lagrange equations of the first kind: index-3 solution, Baumgarte stabilization, solution by block inverses, projection to minimal coordinates.
Lagrange equations of the second kind, generalized coordinates, derivation for point masses, Lagrange function, generalization to rigid bodies.
Hamiltonean equations, generalized impulses, general form of kinetic energy, derivation from Lagrange equations, canonical equations of Hamilton, cyclical coordinates.
Nonholonomic systems: Appell’s equations, derivation with Lagrange multipliers, application to single wheel and sphere on rotating plane.