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modelling : physics II

multiple body interaction

gravitation

(1.1)
F = Gm1m2/r2,
(1.2)
F12 = -F21 = Gm1m2r/r3,

  • G is the gravitational constant, that is approximately G = 6.67 10-11 N m2 kg-2,
  • and r is the absolute value of r.

gravitation - pitfalls

springs

(2.1)
F = C(x-l),
(2.2)
F = C(x- (lx/x)).

  • C is the spring constant with unit [kg s-2],
  • l is the rest length of the spring, and
  • x is the absolute value of x.

  • Car simulation to get accurate suspension reactions,
  • Cloth simulation. Connect springs over a 2d mesh and you get a very pleasent tissue. Search the web for cloth simulation [verlet integration] to see how this works, or have a look at hugo elias' website.
  • Water surface waves. Use a cloth simulation and reduce damping as good as possible and you will get a wavy water surface.

springs - pitfalls

(3.1)
F = C(x-l),
(3.2)
d2x/dt2 = F/m = C/m (x-l).

This differential equation leads to an oscillating system with a frequency of
(3.3)
f = √(C/m).

momentum and energy

the real truth - damping

  • static friction occurs when two objects are not moving relative to each other (pen on a book).
  • dynamic friction occurs when two objects are moving relative to each other and rub together.
  • rolling friction occurs when two objects are moving relative to each other and one is rolling on the other.
  • air friction, wind resistance occurs when one object is moving in a viscous aether.
(4.1)
Ff = μf Fp,
(4.2)
Fair = -cv.
(4.3)
Fair = -c1v -c2v2 -... .

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