Finding angular displacement from displacement vectors

39 Views Asked by At

I apologise in advance if the question is not clear. Suppose I have 4 points on the X-Y plane. Their relative positions with respect to each other are fixed. So any 2 points will have a fixed distance away from each other. In a short time interval, the X-Y plane undergoes a small rotation about a certain unknown point resulting in the displacement of the 4 points as shown in the image attached. If the displacement vectors of the 4 points are given, is it possible to calculate the angle of rotation of the X-Y plane? The axis of rotation is unknown.An illustration of what I mean can be found here Ideally I wish to find a mathematical expression with the displacement vectors with which i can compute the angular displacement.

1

There are 1 best solutions below

3
On

Hint:

The center of rotation is the common point of the perpendicular bisectors of the segments from a starting position of a point to the displaced position.

Use this point as center of a reference frame with an axis that passe thorough one of the points and find the angle of rotation.