Calculus of Variations: Euler's Elastica

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Explores the buckling phenomenon in straight beams due to material breakage or buckling stress being exceeded.

Introduces structural mechanics concepts like distributed loads, centroids, and equilibrium in 2D and 3D.

Explores the calculus of variations and Euler's Elastica in the context of beam equilibrium and inextensible elastic curves under large rotations.

Introduces constraints, Lagrange multipliers, and generalized coordinates in physics.

Explores virtual work in structural mechanics, stability criteria, reaction load calculations, and mechanical systems with springs.

Covers linear elasticity in 3D, focusing on beam bending and stress-strain behavior of materials.

Covers advanced topics in beam bending, stress tensors, elasticity, and Atomic Force Microscopy.

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Covers the analysis of internal forces in beams and deformation under loads.