Shahada ya kwanza (mwanzo)Applied MathematicsImepangwa
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
Somo la mada hii bado halijaandikwa. Muhtasari ulio hapa chini ni sehemu ya ramani ya mtaala na haujakaguliwa.
Inajengwa juu ya
Masharti ya awali ya lazima 38 (hadi chini kabisa)
Utajifunza
- 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.
Fasili
- 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.
Nadharia
- 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).
Mawazo potofu ya kawaida
- Thinking a force is needed to keep an object moving at constant velocity.
- Confusing mass with weight.
Ugunduzi wa hiari
- Smooth manifolds Configuration spaces are manifolds, and Hamiltonian mechanics lives on cotangent bundles with their symplectic structure.
Njia za kujifunza
Usomaji zaidi
- V. I. Arnold, Mathematical Methods of Classical Mechanics
- John R. Taylor, Classical Mechanics (2005)