Weakly Nonlinear Analysis: Multiple Time Scale Expansion

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Covers geometric constraints, work, kinetic energy, and power, including force constraints and small oscillations.

Explores stellar orbits in rotating potentials, focusing on surfaces of section, integrals of motion, and stability around Lagrange points.

Explores the stability of orbits, effective potential shape, and resonances in stellar dynamics.

Explores forces, motion equations, tension, pendulum oscillation, and friction elimination in physical scenarios.

Explores stability, resonance, damping effects, and forced oscillations in harmonic systems.

Explores linear response in dynamical systems, emphasizing fractional derivatives and expanding unimodal maps.

Explores harmonic oscillators, Hooke's Law, and elasticity in relation to force and spring elongation.

Explores the mathematical pendulum, small oscillations, harmonic oscillator, and integration of the equation of motion.

Explores angular momentum, center of mass movement, and Coriolis force impact on Earth's dynamics.