Getting the velocity vector from position vectors

Question

I looked at a bunch of similar questions, and I cannot seem to find one that particularly answers my question. I am coding a simple 3d game, and I am trying to allow the player

Answer 1

basic Newtonian/D'Alembert physics dictate:

derivate(position)=velocity
derivate(velocity)=acceleration

and also backwards:

integrate(acceleration)=velocity
integrate(velocity)=position

so for your engine you can use:

rectangle summation instead of integration (numerical solution of integral). Define time constant dt [seconds] which is the interval between updates (timer or 1/fps). So the update code (must be periodically called every dt:

vx+=ax*dt;
vy+=ay*dt;
vz+=az*dt;
 x+=vx*dt;
 y+=vy*dt;
 z+=vz*dt;

where:

• a{x,y,z} [m/s^2] is actual acceleration (in your case direction vector scaled to a=Force/mass)
• v{x,y,z} [m/s] is actual velocity

• x,y,z [m] is actual position

  1. These values have to be initialized a,v to zero and x,y,z to init position
  2. all objects/players... have their own variables
  3. full stop is done by v=0; a=0;
  4. driving of objects is done only by change of a
  5. in case of collision mirror v vector by collision normal

  and maybe multiply by some k<1.0 (0.95 for example) to account energy loss on impact

You can add gravity or any other force field by adding g vector:

vx+=ax*dt+gx*dt;
vy+=ay*dt+gy*dt;
vz+=az*dt+gz*dt;

also You can add friction and anything else you need

PS. the same goes for angles just use angle/omega/epsilon/I instead of x/a/v/m

to be clear by angles I mean rotation (pitch,yaw,roll) around mass center