Fermat's principle

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

Explores geodesics as locally shortest paths and defines surface area using parametric squares.

Explores the benefits of sheathing optical fibers and fundamental wave propagation principles.

Covers the derivation of boundary conditions in mechanics of slender structures, focusing on total energy variation and equilibrium equations.

Explores equilibrium positions, lineic density, and the principle of least action in analytical mechanics.

Explores the principle of least action in mathematics and its application to functional branches.

Covers the derivation and application of Euler-Lagrange equations for optimization problems in mathematical analysis.

Discusses the application of action principles in classical field theory, focusing on Lagrange and Hamiltonian formulations.

Explores Hamilton's formalism, canonical equations, and Poisson brackets in classical and quantum mechanics.

Explores the superposition and interference of electromagnetic waves, discussing energy redistribution and standing waves.