Variational Calculus and Least Action Principle

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Explores symmetry, Noether's theorem, and conservation laws in physics, emphasizing the role of time and the Hamiltonian.

Explores Hamiltonian formulation and its equivalence with Euler-Lagrange equations, illustrated through examples.

Analyzes the motion of a ball on a hemisphere surface with forces and equations of motion.

Explores the Euler-Lagrange equation, convexity, and saddle point problems in variational calculus.

Explores generalized coordinates, constraints, equilibrium points, and stability in mechanics using elegant polar coordinates.

Introduces field theory, focusing on density, springs, canonical transformations, and the principle of least action.

Covers the Euler-Lagrange equation in Sobolev spaces and discusses minimization, convexity, and weak forms.

Covers Lagrangian mechanics, a method simplifying equations of motion by focusing on energy concepts and generalized forces in complex systems.

Covers the limitations of Lagrange formalism and the transition to Hamiltonian formalism for dynamic variables.

Explores algebraic topology and differential geometry in understanding robot dynamics and global behavior.