Concept

Rigid transformation

Related lectures (31)

Covers the analysis of static (rigid) structures, including equilibrium and free-body diagrams.

Explores projections on lines and symmetries in 2D space, emphasizing fixed points and symmetric matrices.

Covers the analytical expression of orthogonal projections and reflections in 2D space.

Explores local frames in navigation and cartography, emphasizing mathematical expressions and spatial relationships.

Explores Coxeter groups, reflections, fundamental regions, and classification by Coxeter graphs.

Explores the concept of inversion relative to a circle and its applications in constructing orthogonal circles.

Explores geometric examples of triangles and functions, demonstrating the variation of x and y within defined ranges.

Reviews Coxeter groups, reflections, rotations, and fundamental regions in finite orthogonal transformations.

Covers 3D rotations, quaternions, and matrices of direction cosines, providing an elegant solution to the limitations of rotation matrices.

Explores geometric quantization in representation theory, focusing on SO3(R) acting on R³ and homogenous polynomials.

Explores the complexity of rotations in 3D space, covering moment of force, energy equivalence, and cross product matrices.

Covers the conversion and applications of spherical coordinates in mathematical and physical contexts.

Covers the concept of rigid displacement and potential energy, emphasizing continuity between elements and the importance of conforming to the mesh.

Explores virtual displacements, reaction forces, and work on rigid bodies.

Explores the normalization of three reflection planes in geometry through rotor-reflections and glided reflections.

Covers the principles of system equilibrium in 3D and the calculation of resultant forces and couples.

Covers 2D transformations, linear maps, matrices, affine transformations, and orthogonal transformations.

Covers the classification of forces, resultant, and systems of forces in 2D and 3D.

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Explores the mechanics of a dumbbell system on a frictionless surface, covering kinematics, forces, dynamics, and equilibrium conditions.