
Comprehensive exploration of rigid body dynamics, covering mass distribution, center of mass calculation, Newton-Euler equations, and rotational motion, with practical examples and mathematical formulations.

Explore center manifolds in Hamiltonian systems and PDEs, including Lorenz system bifurcation, unstable directions, and applications to flame front evolution and celestial mechanics.

Explore periodic systems, parametric resonance, and the Mathieu equation. Learn about resonance tongues, stability analysis, and the fascinating Kapitza pendulum phenomenon in nonlinear dynamics.

Explore integrable and non-integrable Hamiltonian systems, KAM theory, Poincaré sections, and Poisson brackets in this advanced dynamics lecture, offering insights into complex nonlinear systems and their behavior.

Explore gravity gradient effects on spacecraft stability, including Euler equations, pitch stability, torque equilibrium angles, and applications to the International Space Station.

Comprehensive exploration of Euler's equations for rigid body dynamics, covering derivation, analysis, and practical applications through various examples like spinning tops and fidget spinners.

Example calculations for center of mass and moment of inertia matrix in space vehicle dynamics. Covers planar rigid bodies, composite shapes, and practical applications using integrals and common approximation methods.

Explore moment of inertia matrix calculation, principal axis frame, and their significance in rigid body dynamics. Includes MATLAB demonstration for practical application in spacecraft attitude control.

Explore generating functions for canonical transformations in Hamiltonian systems. Learn about harmonic oscillator examples, near-identity transformations, and connections to quantum mechanics and gauge invariance.