4 ms·
> The planet’s position and momentum can be described by six numbers, three for each property. If you represent each of the different configurations of the plan
by smitty1e 5y ago
> The planet’s position and momentum can be described by six numbers, three for each property. If you represent each of the different configurations of the planet’s position and momentum as a point with six coordinates, you’ll create the phase space of the system. In this case, it has the shape of flat six-dimensional space. The motion of a single planet can be represented as a line weaving through this space.
Sounds like ephemeris?
https://en.m.wikipedia.org/wiki/Ephemeris https://en.m.wikipedia.org/wiki/Ephemeris
- BizarroLand 5y agoThere are a decent amount of symmetries between old ideas and the newest accepted theories. The good ones were typically drawing from the same well, just not able to get to the source.
- kmill 5y agoIn this case it's a description of the 6-dimensional coordinates used in Lagrangian mechanics, which dates to the late 1700s. https://en.wikipedia.org/wiki/Lagrangian_mechanics https://en.wikipedia.org/wiki/Lagrangian_mechanics https://en.wikipedia.org/wiki/Position_and_momentum_space https://en.wikipedia.org/wiki/Position_and_momentum_space The symplectic geometry from the article is an abstract version of ideas from Hamiltonian mechanics, which is from the early 1800s. https://en.wikipedia.org/wiki/Hamiltonian_mechanics https://en.wikipedia.org/wiki/Hamiltonian_mechanics
- dls2016 5y agoF=ma and you need initial conditions on position and velocity to pin down a trajectory… you can always apply a change of coordinates (e.g. ephemeris) to make computation easier in some specific case.