Constraints, Power, Work, and Kinetic Energy

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Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Explores Legendre functions of the second kind and spherical harmonics properties and relationships.

Explores work, kinetic energy, forces, and energy conservation in mechanical systems.

Explores polynomial approximation with orthonormal bases and orthogonal projection methods.

Explores the dynamics of a pendulum, emphasizing equilibrium conditions and kinetic energy calculations for different points.

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Explores kinetic energy, work, and forces, focusing on the role of normal forces and energy modification.

Explores the conservation of energy in pendulum systems and work calculations.

Explores momentum, impulse, work, energy, and angular momentum in advanced physics.

Covers the concept of mechanical energy conservation and angular momentum in different systems.