Lectures related to Small Rotations and Angles

Explores isometries, distinguishing between rotations and reflections, and the preservation of orientation in geometric transformations.

Covers the preservation of isometry by rotations and symmetries.

Explores the synthesis of plane isometries and their composition through axial reflections, rotations, translations, and glided reflections.

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

Covers the concept of orientation in the plane and transformations using matrices.

Covers the geometric definition of rotations in 2D and analytical expressions for rotations using matrices.

Covers attitude and orientation in rotations, including small angles and orthonormal properties.

Delves into modern geometry, covering transformations, isometries, and symmetries.

Explores homotheties and translations in geometry, focusing on preserving alignment and distances.

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

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

Explores the transformation of constraints and deformations in materials, focusing on stress analysis and tensor diagonalization.

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

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

Covers expressing sums and products using trigonometric functions step by step.

Explores Rabi oscillations in quantum information, focusing on spin dynamics and Hamiltonian evolution.

Covers the basics of kinematics, including joint coordinates, operational variables, wrist configurations, and geometric models.

Covers the topic of conformal transformations, including translations, dilations, rotations, and the conformal algebra.

Explores trigonometric addition and subtraction formulas, demonstrating their application in calculating trigonometric values efficiently.

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