3 ms·

When just doing point gravity dynamics (no friction, collision etc) energy and momentum take care of themselves as long as the math is clean. I say this confide

When just doing point gravity dynamics (no friction, collision etc) energy and momentum take care of themselves as long as the math is clean. I say this confidently because I made a solar system simulation[1] with no attention to conservation of energy at all. In practice Star systems also shed large amounts of angular momentum through solar wind[2], but I expect this is often not modelled. Climate models are an entirely different matter and with respect, there is a disconnect with your scepticism of them for this matter. [1] https://strainer.github.io/fancy#00 https://strainer.github.io/fancy#00 [2] http://farside.ph.utexas.edu/teaching/plasma/Plasmahtml/node69.html http://farside.ph.utexas.edu/teaching/plasma/Plasmahtml/node...

nonbel 9y ago
It says in your readme[1] though that your solar system simulation simulation is off by 70k km (regarding Earth orbit) after only 1 year relative to the JPL ephemerides, for "unknown reasons". I don't see how you can use that to justify not checking for conservation of momentum/energy. I also do not understand your final sentence. [1] https://github.com/strainer/fancy https://github.com/strainer/fancy
- strainer 9y ago
  Come on it doesnt say "unknown reasons" it says the "It is possible the discrepancy is due to the limitation of javascripts 64bit FP numbers rather than subtle algorithmic or physics error" 70k km / a year (on a billion km long orbit) was a lot closer than I had hoped for, considering its a 64 bit newtonian model. But this is beside the fact that having worked on the project a fair bit, I understand that any model adjustments to conserve energy or momentum are non-physical 'fudges' to correct deficiencies of the model. There are no laws of physics dedicated to adjusting energy, momentum, information in order to conserve them. They are conserved by a mathematical correctness of every physical law - a proper account of that eludes me, but it is certainly explained somewhere.
  - nonbel 9y ago
    Right, you don't know how much error the floating point error accounts for. You also brought up loss of angular momentum to solar wind, etc. These are all just speculations. That may be fine for the purposes of your simulation, but not for predicting if asteroids will impact the earth or the influence of human activity on Earth's climate. Also, I know you are supposed to use a symplectic integrator to ensure conservation of energy when doing these simulations, so it is not somehow hardcoded into the laws, eg: https://en.wikipedia.org/wiki/Leapfrog_integration https://en.wikipedia.org/wiki/Leapfrog_integration
    - strainer 9y ago
      We could certainly calculate how much error was introduced by rounding, if we had the time and inclination. It is useful to understand that about numerical modelling, it should not be necessary to accept any indeterminable discrepancies. Conservation of energy, momentum, information is hardcoded into all known laws of Physics. It is our integration algorithms which do not all ensure conservation of information - but that is carefully achievable with basic first order schemes, such as Verlet and leapfrog integration.
      - nonbel 9y ago
        >"Conservation of energy, momentum, information is hardcoded into all known laws of Physics. It is our integration algorithms which do not all ensure conservation of information - but that is carefully achievable with basic first order schemes, such as Verlet and leapfrog integration." I am not sure about "conservation is encoded" part, but I can believe it. Either way, in practice the simulations will encounter issues along these lines if they are not careful. For example, I left your simulation running for what amounted to ~120 yrs and saturn lost all her moons. This is the best pic I could get, sorry (hopefully it is reproducible): https://i.imgur.com/C7emd28.png https://i.imgur.com/C7emd28.png Since you do not report anything about conservation of energy/momentum, how do we know that isn't the problem?
        strainer 9y ago

nonbel 9y ago

It says in your readme[1] though that your solar system simulation simulation is off by 70k km (regarding Earth orbit) after only 1 year relative to the JPL ephemerides, for "unknown reasons". I don't see how you can use that to justify not checking for conservation of momentum/energy. I also do not understand your final sentence. [1] https://github.com/strainer/fancy https://github.com/strainer/fancy

strainer 9y ago
Come on it doesnt say "unknown reasons" it says the "It is possible the discrepancy is due to the limitation of javascripts 64bit FP numbers rather than subtle algorithmic or physics error" 70k km / a year (on a billion km long orbit) was a lot closer than I had hoped for, considering its a 64 bit newtonian model. But this is beside the fact that having worked on the project a fair bit, I understand that any model adjustments to conserve energy or momentum are non-physical 'fudges' to correct deficiencies of the model. There are no laws of physics dedicated to adjusting energy, momentum, information in order to conserve them. They are conserved by a mathematical correctness of every physical law - a proper account of that eludes me, but it is certainly explained somewhere.
- nonbel 9y ago
  Right, you don't know how much error the floating point error accounts for. You also brought up loss of angular momentum to solar wind, etc. These are all just speculations. That may be fine for the purposes of your simulation, but not for predicting if asteroids will impact the earth or the influence of human activity on Earth's climate. Also, I know you are supposed to use a symplectic integrator to ensure conservation of energy when doing these simulations, so it is not somehow hardcoded into the laws, eg: https://en.wikipedia.org/wiki/Leapfrog_integration https://en.wikipedia.org/wiki/Leapfrog_integration
  - strainer 9y ago
    We could certainly calculate how much error was introduced by rounding, if we had the time and inclination. It is useful to understand that about numerical modelling, it should not be necessary to accept any indeterminable discrepancies. Conservation of energy, momentum, information is hardcoded into all known laws of Physics. It is our integration algorithms which do not all ensure conservation of information - but that is carefully achievable with basic first order schemes, such as Verlet and leapfrog integration.
    - nonbel 9y ago
      >"Conservation of energy, momentum, information is hardcoded into all known laws of Physics. It is our integration algorithms which do not all ensure conservation of information - but that is carefully achievable with basic first order schemes, such as Verlet and leapfrog integration." I am not sure about "conservation is encoded" part, but I can believe it. Either way, in practice the simulations will encounter issues along these lines if they are not careful. For example, I left your simulation running for what amounted to ~120 yrs and saturn lost all her moons. This is the best pic I could get, sorry (hopefully it is reproducible): https://i.imgur.com/C7emd28.png https://i.imgur.com/C7emd28.png Since you do not report anything about conservation of energy/momentum, how do we know that isn't the problem?
      - strainer 9y ago