Circular motion at constant speed I have a question. I have an algorithm that computes the trajectory of a body moving in a circle. The program repeats the following at short intervals to update the body's X and Z positions:
$$x = \mathrm{X_c} + R\cos\left(\frac{2\pi}{T}t\right)$$
$$z = \mathrm{Z_c} + R\sin\left(\frac{2\pi}{T}t\right)$$
$X_c$ and $Z_c$ are the x and z positions of the rotation axis, respectively. The $t$ value is increased by $1$ with each update. In turn, $T$ means the time it takes the body to complete one circle. The problem is that changing the radius $R$ value changes the speed of the body. I want a constant speed, independent of the radius. How can I get rid of the $T$? Ideally, the speed should be predefined. This means that regardless of the radius of the circle, the body should always move at a fixed speed. Is there a way? I will be grateful for your help.

Suppose you want the speed of the body to be $v$.
The amount of time that passes while the body travels once around the circumference of a circle of radius $R$ will then be
$$ T = \frac{2\pi R}{v}. $$
Plug this into your formulas:
$$ \frac{2\pi}{T} = \frac{2\pi}{\left(\frac{2\pi R}{v}\right)} = \frac vR , $$
$$x = \mathrm{X_c} + R\cos\left(\frac vR t\right),$$
$$z = \mathrm{Z_c} + R\sin\left(\frac vR t\right).$$
