Nonlinear beam theoryCovers strain-displacement relations, equilibrium equations, and energy functional in nonlinear beam theory with small strain and moderate rotation.
Polar Decomposition TheoremExplains the Polar Decomposition Theorem, which isolates stretching from rotation to prevent stress induction in the body.
Nonlinear Beam TheoryCovers stress-strain relations, constitutive relations, and buckling of a circular ring in nonlinear beam theory.
3D Rotations and QuaternionsCovers 3D rotations, quaternions, and matrices of direction cosines, providing an elegant solution to the limitations of rotation matrices.
Systems of Forces in 3DExplores systems of forces in three dimensions, emphasizing moments and couples, equilibrium, and scalar components.
Isometries in Euclidean SpacesExplores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.
