Ungh. I've been working on this problem for something like a month, and no solution. I'm beginning to suspect that it's well outside my current mathematical ability.

Basically, it's a physical problem. You have a spaceship, S, that is rotating, and accelerating its rotation. It is also accelerating 'straight forward', where straight forward depends on what direction it's facing, of course.

Mathematically:

domega/dt=alpha
dtheta/dt=omega
dv/dt=A(i*sin(theta)+j*cos(theta))

A, alpha constant with time. (i and j are the unit vectors in the x and y axis, respectively).

I'm trying to get a function for s. Simple enough, right? Just integrate the third function. Problem - theta gets ugly.

omega=alpha*t + omega(0)
theta=0.5*alpha*t**2 + omega(0)*t + theta(0)

Subbing that into dv/dt gives me an interestingly difficult equation to integrate - twice - that is, the sin (or cos) of a quadratic in the variable being integrated over.

I've been told that there may not be a solution in elementary functions - which sounds strange, to me, given that it's a simple physical system, so I'd expect it to give me a calculatable result. I do need to solve this in the general case to do what I want with this function - namely, use it in a game.

Any thoughts from some more mathematically-inclined members?