- #1
schaefera
- 208
- 0
If you parameterize an ellipse such that x=acos(t) and y=bsin(t), then you quite easily get the relations:
r={acost, bsint}
v={-asint, bcost}
a={-acost, -bsint}
But my issue is that now, if I think of the equations as representing the motion of a planet about its sun, the acceleration vector listed above always points toward the center of the ellipse and not toward the ellipse's focus. (Take, for example, t=pi/2... with this, the position is along the y-axis at a distance b, and acceleration points toward the origin, not the ellipse's focus).
That is, the acceleration is always directed normal to velocity, which should only happen in a circle... so what is wrong with my math?
r={acost, bsint}
v={-asint, bcost}
a={-acost, -bsint}
But my issue is that now, if I think of the equations as representing the motion of a planet about its sun, the acceleration vector listed above always points toward the center of the ellipse and not toward the ellipse's focus. (Take, for example, t=pi/2... with this, the position is along the y-axis at a distance b, and acceleration points toward the origin, not the ellipse's focus).
That is, the acceleration is always directed normal to velocity, which should only happen in a circle... so what is wrong with my math?