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Lecture
Spherical Coordinates: Conversion and Applications
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Kinematics: Position, Velocity, Acceleration
Covers the fundamental concepts of kinematics, including position, velocity, and acceleration in different coordinate systems.
Rotations: Fixed Points and Spherical Coordinates
Covers rotations around fixed points and spherical coordinates, discussing cinematic moments and angular velocity.
Coordinate Vector Operations
Explores coordinate vector operations, from digitizing points to transforming and manipulating geometric spaces using coordinates.
Inertial Frame: Earth's Reference Systems
Covers Earth's inertial frames, specific forces, and the Vernal Equinox.
Kinematics: Reference Frames and Coordinates
Introduces reference frames, coordinates, point mass, trajectory, velocity, acceleration, and motion with constant acceleration.
Cylindrical and Spherical Coordinates
Covers cylindrical and spherical coordinates as alternatives to Cartesian coordinates, focusing on their definitions, coordinate lines, and vector projections.
Coordinate Changes: Spherical System
Explores differentiability, coordinate changes, Jacobian determinant, gradient transformation, and chain rule.
Translations and Homotheties
Covers translations, homotheties, and their analytical expressions, emphasizing stability by composition.
Integration and Transformations
Covers the calculation of definite integrals and different coordinate systems.
Cinématique: Polar Coordinates Part 1
Covers the basics of polar coordinates and their application in kinematics.