3 ms·
> So if a simulator shows a deviation from this constant sum, there's something wrong with the simulator and/or the underlying mathematics. Not necessarily so
by santaclaus 10y ago
> So if a simulator shows a deviation from this constant sum, there's something wrong with the simulator and/or the underlying mathematics.
Not necessarily so -- many (most) discrete integrators do not exactly conserve the Hamiltonian. In fact, large classes of geometric integrators yield noticeable (but bounded) amounts of 'noise' on top of the true Hamiltonian.
- lutusp 10y ago>> So if a simulator shows a deviation from this constant sum, there's something wrong with the simulator and/or the underlying mathematics. > Not necessarily so But the "constant sum" I refer to is the sum of gravitational potential energy and kinetic energy in the system. If that were not true, if the sum were not a constant (and remembering this is an ideal model without friction), then energy would not be conserved. So, yes, necessarily so.