Primeros años de universidadApplied MathematicsPlanificado
Classical mechanics
Newton's laws as differential equations, conservation of energy and momentum, oscillators, central forces and Kepler's laws, and an introduction to Lagrangian mechanics.
math.applied.classical-mechanics
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Se basa en
Requisitos previos obligatorios, hasta el fondo: 38
Aprenderás a
- Solve the equations of motion of projectiles and of harmonic oscillators, with and without damping.
- Use conservation of energy and angular momentum to analyse motion under a central force and derive Kepler's laws.
- Derive equations of motion from a Lagrangian using the Euler–Lagrange equations.
Definición
- Newton's second law: F = ma, where the acceleration a is the second derivative of position.
- A force field F is conservative if F = −∇V for some potential V.
- The Lagrangian of a system is L = T − V, kinetic energy minus potential energy.
Teorema
- For conservative forces the total energy T + V is conserved.
- Under a central force, angular momentum is conserved and the motion stays in a plane.
- Bound orbits under an inverse-square attractive force are ellipses (Kepler's first law).
Errores frecuentes
- Thinking a force is needed to keep an object moving at constant velocity.
- Confusing mass with weight.
Descubrimientos opcionales
- Smooth manifolds Configuration spaces are manifolds, and Hamiltonian mechanics lives on cotangent bundles with their symplectic structure.
Itinerarios de aprendizaje
Lecturas complementarias
- V. I. Arnold, Mathematical Methods of Classical Mechanics
- John R. Taylor, Classical Mechanics (2005)