How can I find the collision time of 2 ellipsoids that rotate

In summary, there are two ellipsoids, A and B, with equations for their shapes and both rotating around different axes with infinite speed. The question is how to determine the collision time between the two ellipsoids, but this may be unclear due to the infinite speeds involved. It may be more appropriate to ask for the fraction of time that the two figures have some intersection.
  • #1
Guy Ab
1
0
I have 2 ellipsoids:

Ax^2/a^2+Ay^2/b^2+Az^2/c^2=1; (*a,b,c>0 constants*)
Bx^2/a^2+By^2/b^2+Bz^2/c^2=1;
Ellipsoid A rotates around axis [wax;way;waz] (unit vector) with an infinite speed;
Ellipsoid B rotates around axis [wbx;wby;wbz] (unit vector) with an infinite speed;
[Dx;Dy;Dz] is the vector from ellipsoid A center to ellipsoid B center;
The velocity of ellipsoid A center is [VAx;VAy;VAz];
The velocity of ellipsoid B center is [VBx;VBy;VBz];

How can I find the collision time?
 
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  • #2
You should clarify the question.

How does it make sense to ask for a collision "time" when things are happening at "infinite" speed? Are you seeking "the fraction of time" that two figures would have some intersection?
 

1. How can I determine the initial position and velocity of the ellipsoids?

In order to find the collision time of two rotating ellipsoids, you first need to know their initial positions and velocities. This can be done by analyzing the geometry and dynamics of the system and taking into account any external forces acting on the ellipsoids.

2. What equations or mathematical models can I use to calculate the collision time?

There are various mathematical models and equations that can be used to determine the collision time of two ellipsoids. The most commonly used methods include the Newton's laws of motion, the conservation of energy, and the principle of virtual work.

3. How does the rotational motion of the ellipsoids affect the calculation of the collision time?

The rotational motion of the ellipsoids plays a crucial role in calculating the collision time. This is because the rotation of the ellipsoids changes their positions and velocities over time, making the collision time a dynamic and constantly changing value.

4. Can the shape and size of the ellipsoids impact the calculation of the collision time?

Yes, the shape and size of the ellipsoids can greatly affect the calculation of the collision time. This is because the collision time is dependent on the distance between the ellipsoids and their orientation, which can be influenced by their shape and size.

5. Are there any simplifications or assumptions that can be made in order to calculate the collision time?

Yes, there are some simplifications and assumptions that can be made in order to make the calculation of the collision time easier. For example, assuming the ellipsoids are perfect spheres or neglecting any external forces can simplify the equations and make the calculation more manageable.

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