Physics in Action |
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Interactive Physics | 3D Modern Physics I: Rotation | Physics in Virtual Reality | Physics Simulations using Swing/Java2D |
Non-interactive Physics Demo
Brief Discussion |
The Equations (ODE2): |
d^2 x1/dt^2 = - k1*x1 - k2*(x1 - x2) - 9.8*fk*dx1/dt; d^2 x2/dt^2 = - k1*x2 - k2*(x2 - x1) - 9.8*fk*dx2/dt; |
The Initial Conditions: |
x1 = x1(0); x2 = x2(0); v1 = 0; v2 = 0; |
Mass and Coefficients Convensions: |
We have set m1 = m2 = 1 (dimensionless). This means we have also set: our k1 = k1/m and our k2 = k2/m, where m is the mass of each cart |
Reference: |
Grant R. Fowles and George L. Cassiday: Analytical Mechanics, 5th Edition, Saunders College Publishing, section 11.3, pp. 382. |
After we have found the best fitting K and Tau, then we can simulate some Magnus motion which is very hard to do in a real Lab. Here we let K = 0.12, Tou = 2.5 sec, Q0 = π/4, and let v0 = 30m/s and 45 m/s respectively. The animations are:
Traveling Wave and Vibtation Along a String
Magnus Flow: Magnus flow near a spinning cylinder
Physics Simulations Using JApplet/Swing/Java2D |
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