What are phase space coordinates and how do you plot them?

[MattIverson]

Homework Statement

I have phase space coordinates (x0,y0,z0,vx,vy,vz)=(1,0,0,0,1,0). I need to analytically show that these phase space coordinates correspond to a circular orbit.

Homework Equations

r=sqrt(x^2+y^2+z^2) maybe?

The Attempt at a Solution

My core problem here is maybe that I don't understand what a phase space is on a deep level. I've read that each of the coordinates corresponds to a motion, but I don't really understand what that means.

My first thought was that this corresponds to a circular orbit because if you imagine an x,y,z axis and you put a point at (1,0,0) then move that point in the y direction (because there's a 1 in the vy spot) you'll get a circular movement. Not sure if that makes sense...

 

[BvU]

show that these phase space coordinates correspond to a circular orbit

You'll need a bit more than you have posted now. A point in phase space is just what you quote: a position (0,0,0) and a velocity (0,1,0), in your case at some t= t₀.

These two can be on an infinite amount of circles, but I suppose there is something in your complete problem statement that refers to a circle around the origin in the x,y plane with radius 1 ?

To keep the point on a circle you need some force, a constraint or so.