Andrew Coppin wrote:
> Now... what happens if my moving particle is contraigned to a sphere? In
> other words, there is a mass-less inextensible "string" teathering it to a
> fixed point in space. (The force will always be acting in such a way that
> the "string" remains taut - there is no possibility of it 'going slack',
> which makes things a bit easier.)

If the string remains taut the part of the force that is colinear with the 
string will get compensated. In other words the particle will always move 
in the plane perpendicular to the string! This means that all you have to 
do is to project your force into this plane. 

Given n the unit vector which is colinear with the string and f the vector 
of your force, the projection f' of f into the plane is given by:

 f' = f - n*vdot(n,f)

An example: is the string along the y-axe then the normal vector is <0,1,0> 
and therefore:
 f' = f - <0,1,0>*vdot(<0,1,0>,f)
Now vdot(<0,1,0>,f) is equal to f.y and hence:
 f' = f - <0,f.y,0> = <f.x, 0, f.z>

You could also check if the string remains taut by looking if vdot(n,f) is 
negative or positive (you have to fix the direction of n (that means choose 
if it points from from string base to particle or the other way round).

Hope I got this right

- Micha

-- 
objects.povworld.org - The POV-Ray Objects Collection
book.povworld.org    - The POV-Ray Book Project

Post a reply to this message