Quaternions and spatial rotation

Related lectures (31)

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

Covers the concept of vector rotation in kinematics and the derivative of a vector with constant norm.

Explores angular momentum, rotational dynamics, and moment of inertia for solids.

Covers the preservation of isometry by rotations and symmetries.

Explores the analysis of motion in solid mechanics, covering velocity, acceleration, and kinematics of solid bodies.

Explores the symmetries of Navier-Stokes equations in periodic boxes, including translations, transformations, rotations, and scaling.

Explores changing bases for rotations, orthogonal planes, and vector transformations under rotation.

Covers the laws of transformation of speeds and accelerations, including the rotation of points and dynamic movement principles.

Covers the composition of geometric transformations in 2D, focusing on rotations and reflections to achieve specific results.

Explores symmetries in Newtonian mechanics and wave equations, highlighting their significance in understanding physical laws.

Covers the concept of 2D rotations and their analytical expressions.

Explores normal acceleration, spatial rotations, vector rotation, and angular speed concepts in physics.

Explores the Hamiltonian formalism, conservation laws, preserved quantities, and differential equations in classical physics.

Explores rotation in analytical geometry, including center coordinates and fixed points.

Covers velocity, acceleration, dynamics, moments of inertia, and kinetic energy storage systems.

Explores small rotations, angles, and skew-symmetric matrices in mathematical transformations.

Explores rotation dynamics, gyroscopic effects, and symmetry axes in advanced physics.

Explores the concept of curl in 2D vector fields and its practical applications.

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

Covers cylindrical and spherical coordinates, position, velocity, and acceleration vectors.

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