Calculus of Variations: Euler's Elastica

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Discusses kinematic quantities and linear mass density in examples of metal wires.

Explores beam bending theory, covering moment-curvature relation, pure bending, elasticity concepts, and examples of cantilever beams.

Explores beam buckling, dimensionless analysis, and scalings in mechanics of slender structures.

Covers the mechanics of slender structures, focusing on nonlinear curved beams.

Explores beam bending, moment distribution, and buckling in structural mechanics.

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Discusses equilibrium in three-dimensional systems, focusing on constraints and statical determinacy through practical examples.

Covers the principle of least action, Euler-Lagrange equations, Lagrange multipliers, and variational calculus.

Covers the kinematics and equilibrium equations of Kirchhoff rods, discussing geometric coupling between bending and twist.