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Results tagged with classical-mechanics
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user 13650
Mathematics of classical mechanics, including Hamiltonian mechanics, Lagrangian mechanics, applications of symplectic geometry to mechanics, deterministic chaos, resonance etc.
17
votes
Accepted
Construction of an optimal electron cage
Electrostatic potential is a harmonic function on any region without charges. It has no local minimum, in fact the value at the origin is the average of the potential over a sphere centred at the orig …
- 54.2k
2
votes
underdamped oscillation with quadratic decay
I don't know about "physically driven", but you could try
$$\ddot{u} + 4 t \dot{u} + (4 t^2 + 3) u = 0$$
If you want something autonomous, you might make it
$$ \eqalign{\ddot{u} + 4 v \dot{u} + (4 …
- 54.2k
31
votes
Billiard dynamics under gravity
Here is the rather interesting result I get in Maple for a square of side 1 tilted at 30 degrees, acceleration of gravity = 1, initial position at the top left corner and moving horizontally with spee …
- 54.2k