Lectures related to Initial Alignment: Methods and Strategies

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

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

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

Geometric Nonlinearity: Large Rotations in Structural Analysis

Delves into geometric nonlinearity in structural analysis, emphasizing the impact of large rotations on structural response.

Rotations and Symmetries

Covers the preservation of isometry by rotations and symmetries.

Rotations in Mechanics

Explores rotations in solid mechanics, from two-dimensional to three-dimensional scenarios, emphasizing small angles and different coordinate systems.

Irreducible Representations of Rotations Group

Explores irreducible representations of the rotations group and their mathematical properties.

Complex Numbers: Polar Form, Powers, Roots

Explores complex numbers in polar form, powers, and roots, including trigonometric relationships and rotation matrices.

Symmetries in Mechanics and Wave Equations

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

Geometric Transformations in R2 and R3: Visualizations and Rotations

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

Geometric Transformations Compositions

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

3D Rotations and Quaternions

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

Kinematics Basics: Modeling & Transformations

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

Physics 1: Harmonic Oscillator and Spherical Coordinates

Explores harmonic oscillators, pendulum movement, and spherical coordinates in physics.

Scalar Products in 2D and 3D Geometry

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

Small Rotations and Angles

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

Symmetry Operations in Materials Science

Covers symmetry operations in materials science, including rotations and helical axes.

Equilibrium in 3D: System Isolation and Constraints

Covers the equilibrium conditions in 3D, system isolation, free-body diagrams, and constraints.

Isometries & Orientation in Modern Geometry

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Quantum Information: Rabi Oscillations

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