Helix Trajectory and Coordinate Systems

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Shells I: Mechanics of Slender Structures

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Coordinate Systems: Applications and Transformations

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Kinematics: Position, Velocity, Acceleration

Covers the fundamental concepts of kinematics, including position, velocity, and acceleration in different coordinate systems.

Central Motion: Trajectories and Energy

Explores central motion properties, energy conservation, and trajectory parameter determination based on mechanical energy and angular momentum.

Motion in Three Dimensions

Covers motion in three dimensions, including scalar and vector velocities, acceleration, and curvilinear abscissa.

Circular motion: Concepts and Calculations

Explores circular motion concepts, centripetal force, velocity, and acceleration in different coordinate systems, with a focus on auto racing and Formula 1 tire physics.

Coordinate Systems: Polar, Cylindrical, and Spherical

Explains polar, cylindrical, and spherical coordinates in physics, emphasizing their advantages in simplifying motion analysis.

Helical Curves: Theory and Applications

Explores the theory and applications of helical curves, focusing on circular helices with various parameters.

Spatial Curves: Singularities and Mechanisms

Explores spatial curves, singularities, and mechanisms, analyzing their geometric properties and applications.

Circular motion: Friction and Newton's Laws

Explores circular motion, friction, and Newton's laws in various coordinate systems.