Stellar Orbits: Lagrange Points

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Explores the matter content in the universe, including galaxy mass, dark matter relics, and the history of the universe.

Bifurcations: Flip and Andronov-Hopf

Explores flip and Andronov-Hopf bifurcations, showing how systems change equilibrium points and stability.

Kepler's Laws and Orbital Mechanics

Explores Kepler's laws, orbital mechanics, energy of motion, flight path angles, orbital maneuvers, Hohmann transfers, geostationary orbits, and Lagrange points.

Bifurcations: Introduction

Covers the introduction to bifurcations in dynamical systems, including examples and theorems.

Euler-Lagrange Equation

Covers the Euler-Lagrange equation in Sobolev spaces and discusses minimization, convexity, and weak forms.

Coriolis Effect: Forces and Deviations

Explores the Coriolis effect, explaining forces and deviations in trajectories due to Earth's rotation.

Nonlinear Dynamics: Homoclinic Orbits and Bifurcations

Delves into homoclinic orbits, bifurcations, and limit cycles in nonlinear dynamics.

Variational Methods: Shortest Time Path Problem

Covers variational methods to find the shortest time path for a particle under gravity.

Hamiltonian Formulation and Equivalence with Euler-Lagrange

Explores Hamiltonian formulation and its equivalence with Euler-Lagrange equations, illustrated through examples.

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.