Physics 210

Autumn 2003

Slides Used in Lecture and Other Examples

 

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• Orbit calculation for a central force (of power law -alpha), starting from the first-order differential equation.  (PDF)
• Orbit calculation for a central force (of power law -alpha), starting from the second-order differential equation.  (PDF)
• Simple Euler method for integration of a 1^st-order differential equation with initial value.  (PDF)
• Modified Euler method for integration of a 1^st-order differential equation with initial value.  (PDF)
• 4^th-order Runge-Kutta method for integration of a 1^st-order differential equation with initial value.  (PDF)
• Example C program for Runge-Kutta integration of a 1st-order differential equation with initial value.  (C code)
• 4^th-order Runge-Kutta method for integration of a set of 2 1^st-order differential equations with initial values.  (PDF)
• 4^th-order Runge-Kutta integration of the simple-pendulum equation, starting from the 1^st-order differential equation.  (PDF)
• 4^th-order Runge-Kutta integration of the simple-pendulum equation, starting from the 2^nd-order differential equation.  (PDF)
• Solution of the restricted 3-body problem by Runge-Kutta integration.  (PDF)
• General 3-body problem by Runge-Kutta integration:  FORTRAN code, Example Trajectory, Animation
• Demonstration of Liouville’s theorem for a plane pendulum.  (PDF)
• Integration of the equations of motion of a symmetric top.  (PDF)
• Solution of a coupled-oscillator problem with damping and a driving force.  (PDF)
• Demonstration of chaos in a set of non-linear differential equations (from O.E. Rossler; see Exercise 11.7 in Goldstein).  (PDF)
• Henon-Heiles potential.  Demonstration of a strange attractor.  FORTRAN code, Plots