Mechanics of Kirchhoff Rods I

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Explores the Frenet-Serret formulas for curvature and torsion in three-dimensional space.

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Covers the dimensional reduction in slender structures, constitutive laws, and mechanics of plates and shells.

Examines geometric singularities in architectural design through the analysis of spatial intersections.

Covers 3D linear elasticity, stress, strain, beams' behavior under loads, and torsion.

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

Explores the geometry of parametric curves, covering tangent vectors, curvature, and curve smoothing techniques.

Covers geodesic curves parameterized at constant speed to minimize distances between points.

Explores the mechanics of solids, emphasizing rotation and equilibrium principles.