Lectures related to Vibratory Mechanics: 2 Degrees of Freedom

Circular Motion and Harmonic Oscillator

Explores circular motion, harmonic oscillators, and double springs, elucidating the physics principles behind them.

Material Point Model: Basics

Covers the material point model, initial conditions, and Newton's laws in physics.

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

One Dimensional Harmonic Oscillator

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

Ordinary Differential Equations: Definitions and Examples

Covers ordinary differential equations, their orders, examples, and applications in various fields.

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Canonical Equations: Solutions and Impulses

Explores canonical equations for isolated systems, finding solutions and analyzing impulses.

Harmonic Oscillator: Model & Energy

Explores the harmonic oscillator model, energy treatment, applications, and equations of motion.

Ordinary Differential Equations: Second Order Linear Inhomogeneous

Covers the resolution of second-order linear ordinary differential equations with constant coefficients and a source term.

Projectile Motion: Friction Effects

Explores projectile motion with friction effects and dynamics of polar expeditions.

Differential Equations in Motion

Explores differential equations for motion, including critical damping and damped oscillators, with applications in complex numbers and examples of mass-spring systems.

Cauchy-Euler Equations

Covers the definition and solution of Cauchy-Euler equations, which are second-order differential equations with specific form and solutions.

Canonical Transformations in Analytical Mechanics

Explores canonical transformations, conservation of quantities, and differential equations in analytical mechanics.

Rectilinear Motion: Concepts and Examples

Covers rectilinear motion concepts, including acceleration and differential equations, with examples of uniform motion.

Path Integral Representation of Propagators

Covers the path integral representation of propagators for free particles and harmonic oscillators.

Equations of Motion and Stability

Explores equations of motion resolution, equilibrium points, and stability analysis through small perturbations in a mechanical system.

Differential Equations Solutions

Covers solutions of differential equations with initial conditions and boundedness concepts.

Second Order Equations

Covers second-order differential equations, focusing on finding particular solutions and the general solution.

Law of Hooke Applications: Spring Problems

Explores the application of the law of Hooke to spring problems and solving equations of motion for block-spring systems.

Oscillations libres, ressort

Explores free undamped oscillations in a harmonic oscillator and their graphical representation over time.