Lecture

Rotations: Concepts and Applications

Related lectures (32)

Covers angular momentum in rotations, including preservation of angles and vector products.

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

Explains the inertia tensor, main axes, principal moments, and balancing of rotating solids.

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Explores rotations in two dimensions, covering vector products, angular momentum, and Newton's laws applied to rotational motion.

Covers visualizations in orthonormal bases in R2, focusing on rotations and reflections.

Explores rotations, angular momentum, torque, and moment of inertia in practical applications like MRI and flywheels.

Explores the properties and applications of matrix transpose, including rotations and inverse matrices.

Explores the dynamics of rigid bodies, emphasizing the concept of the center of mass and its applications in equilibrium and rotational motion.

Explores rotation in two dimensions, covering vector products, angular momentum, and kinetic energy of solids.

Explores kinematics and dynamics of rigid bodies, including Euler angles and moment of inertia.

Covers the kinetic energy of a solid and its movement and rotation.

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

Explores changing frames in 2D through translations, rotations, and the introduction of a transformation matrix U.

Explores rotation in two dimensions, equilibrium conditions, angular momentum theorem, and Newton's laws.

Explains the calculation of moment of inertia for rotating objects.

Explores rotational motion, moment of inertia, torque, and static equilibrium in rigid bodies.

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

Explores diagonalization of moment of inertia and principal directions in orthonormal base vectors.

Explains the concept of moment of inertia in rigid body rotation and torque.