Curl in 2D: Understanding Vector Field Rotation

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Rotations: Angular Momentum

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

Analytical Geometry: Rotation and Center

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

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Covers the concept of curl in 3D, a vector operator describing rotation.

Tensor Transformations

Introduces tensor transformations, rotation matrices, and differential operators in mechanics.

Acceleration and Rotation

Explores acceleration derivation, vector rotation, and coordinate systems in rotational motion.

Isometries in Euclidean Spaces

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

Solid Mechanics: Motion Analysis

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

Curve Integrals of Vector Fields

Explores curve integrals of vector fields, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.

Base Change for Rotation: Example

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

Coordinate Systems: Cylindrical, Spherical, Rotations

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