Articles for subject Classical

  • Resonance 2 Oscillators some time ago
    When an oscillator is driven at just the right frequency it hits resonance and absorbs energy from the driving. The details of resonance for a driven and damped harmonic oscillator are explored.
  • Energy of the damped harmonic oscillator is described. The Q of an oscillator.
  • The solution to a damped oscillator with a periodic driving force is derived.
  • The solutions to the harmonic oscillator with a velocity dependant drag force are derived. The relaxation time for the oscillator is defined.
  • The Lotka-Voltera equations are a very simple model of predator-prey dynamics. They lead to oscillatory behaviour in both populations.
  • The Pendulum 2 Oscillators some time ago
    The equations of motion and solutions are derived for the simple pendulum and a general pendulum. Dynamical maps are introduced as a way of handling nonlinear oscillators.
  • The motion for a harmonic oscillator is derived using Newton’s second law. Different parametrizations of the solution, the velocity, acceleration and energy are also determined.
  • An extremely simplified model of a cat (just four masses!) is presented, following Putterman and Raz [Am. J. Phys. 76, 1040 (2008)]. This simple model is enough to show how a deformable body is able to rotate itself despite conserving angular momentum.
  • The equations of motion for a heavy symmetrical top are derived in terms of the Euler angles and using a Lagrangian approach. The solutions are examined numerically.
  • A single object or particle moving under the influence of a central force.
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