Hi,

I'm trying to calculate the position of an object that moves ahead with constant acceleration but that changes its heading at a constant rate. I get a strange result, so I think that I'm missing something. Could you take a look and give me some advice?

The linear velocity of the object is $\displaystyle v = v_0 + a t$, and the heading is $\displaystyle \theta = \theta_0 + \omega t$. The velocity in $\displaystyle x$ is then $\displaystyle v_x = (v_0 + a t) \cos(\theta_0 + \omega t)$.

To simplify, I consider the case with $\displaystyle v_0=0, \theta_0=0, a=1$, so $\displaystyle v_x = t \cos \omega t$.

Then I try to integrate $\displaystyle v_x$ to get the position in $\displaystyle x$, and I get the following:

$\displaystyle x(t) = \frac{\cos \omega t}{\omega^2} + \frac{t \sin \omega t}{\omega}$

My problem is that if now I consider the case where the object moves with constant heading, $\displaystyle \omega = 0$, and I apply the formula above, the result is infinity.

What I am doing wrong here?

Thanks!