I am just wondering if it is possible to calculate/estimate the location of measurement point on a rigid body?

For example, lets say we have a rigid body that is in motion. We attach a sensor, say an accelerometer on the surface of the rigid body. Now can we estimate the location of the accelerometer by using motion equations or just mechanics? The location can be given as a vector from the center of the rigid body for instance. Things we know about the rigid boy are it mass, moment of inertia and rotation rate. Also, the axis of rotation is not at the center of the body



1 Answer 1


Of course this can be done: a rigid body moves, by definition, by Euclidean isomteries, i.e. its motion can be defined by a composition of a translation and a rotation of its orientation. If you know the translation of its center of mass and the rotation of its orientation, then you can work out the position of any point on it at any time by simple geometry.

The translational motion of the center of mass is defined by Newton's second law given the nett force on the body, and the body's rotation about the center of mass is defined by the Euler's second law - that the rate of change of angular momentum equals the nett torque on the system calculated about the center of mass.

  • $\begingroup$ Thanks for the answer. The translational motion of the center of mass is unknown. Also, the rotation is not about the center of mass, but about an axis which is not located at the center of mass. $\endgroup$
    – irobot96
    Commented May 10, 2017 at 6:19
  • $\begingroup$ @uqhi It's easy enough to make the transformations between axes. Is your question how to make them? The translation of the COM is defined by Newton's second law, which means you need to know the forces on the body and an initial velocity. $\endgroup$ Commented May 10, 2017 at 22:16

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