Rotational Computation

[Evlich]

Hello, I am working on a project modeling the solar system and I am having quite a bit of trouble with this rotation thing. If I have a moon that could potentially rotate in three dimentions, how can I calculate the torques on the object. I found an example of how to do it for 2 dimensions that is really good, but I don't understand how I should model it for 3 dimensions. Do I need to keep track of its rotation around the x y and z axis or just its rotation in the xy plane and in the xz plane? And how would I go about computing the torques. The example shows how to do it easily with cross products and stuff, and I kinda understand that, but I can't seem to picture it in 3 dimensions. Thanks a lot for your help.

[Tom Mattson]

You do not have to keep track of the motion. Indeed, your program is supposed to do that for you!

 

I will start with the basic motion: The orbit of the body. After that, we can add rotation if you want. Also, I don't know if you want to include the effect of the rotating bodies bulging in the middle; that will make it more complicated.

 

Anyway...

 

As you are probably aware, the dynamical law governing the system is:

 

(Sum)F=m(d²r/dt²)

 

or, if you prefer torques:

 

(Sum)T=I(d²(theta)/dt²)

 

(sorry, don't know how to make Greek letters).

 

In either case, this is a second order differential equation. That means you need two pieces of initial data, say, the initial position and initial velocity. You will need this information as a vector. In other words, you need all 3 components of the two pieces of information.

 

Once you have that, you can set up the differential equation (you know the force: gravity) and have the computer solve.

[Evlich]

Ok, that is the part that I understand, what I don't understand is will I have to model the torques as rotating around the x, y and z or can you do it with just an xy angle and an xz angle? I have the force as a 3D vector and the distance from the rotation as a 3D vector. I take the cross product and from that I get something, but I am not quite sure what I get. I already have the motion working perfectly in 3D, can you explain how I can get from on instance, to the next. For instance, I know where everything is, how fast it is moving, how fast it is rotating and what it is rotating around, how do I use that to get the torque as a 3D vector (I was only shown the way to get it as a torque in the xy plane). Thanks a lot.