# Impulse required to stop a rotating body

#### cboyce

I have a rigid body rotating in 3D space. I have a torque vector that I want to apply to the rotating body over a given time step. What I want to know is, will the torque be enough to stop the body rotating on any of its axis and reverse direction, and, if so, exactly what would the torque vector be to stop the rotation instead of reverse it. The angular velocity is known, and the inertia tensor is known, so I am calculating the angular momentum as I * w.

The background to this is that I'm simulating the friction of a particular point on a body in space, and often times the torque created by the friction is more than adequate to stop the body from rotating, and if I apply the full friction-caused torque to the body, it actually rotates in the opposite direction, when what I really want to do is simply stop the rotation.

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#### A.T.

if so, exactly what would the torque vector be to stop the rotation instead of reverse it.
Torque is the change of the angular momentum over time. If you know what change of angular momentum you want to achieve (to stop the rotation it is the negative of the current angular momentum) and the time period you want to apply the torque it rather trivial:
Torque = dL / dt

#### cboyce

Thanks for the reply. My problem is that I don't know how to determine if a given torque will stop the rotation over time. I understand how to find out the impulse to stop the rotation completely, but that's not what I necessarily want to do. I've got a torque that's working against the rotation, and at most, I want to stop the rotation rather than reverse it. I was thinking of doing a component-wise comparison, but I'm not sure if that's a valid approach. Basically, something like this:

I have an angular momentum of [1,2,3]. In order to stop the rotation in 1 second, I'd apply a torque of [-1,-2,-3]. But, the torque vector I want to apply is [0,-2,-4]. Would I be able to simply compare components and determine that the force I want to apply without reversing any rotational direction would be [0,-2,-3]?

#### Cleonis

Gold Member
I'm simulating the friction of a particular point on a body in space, [...] if I apply the full friction-caused torque to the body, it actually rotates in the opposite direction, when what I really want to do is simply stop the rotation.
I'm not sure I understand what your goal is. Possibly some information is missing

The whole idea of a simulation is that you set up the equations in such a way that blatantly unphysical outcomes are inherently impossible.

In the case of friction the quick 'n dirty approximation is to make the amount of friction proportional to the velocity. Then by the time the rotation has been reduced to zero the torque is down to zero.

#### A.T.

I have an angular momentum of [1,2,3]. In order to stop the rotation in 1 second, I'd apply a torque of [-1,-2,-3]. But, the torque vector I want to apply is [0,-2,-4]. Would I be able to simply compare components and determine that the force I want to apply without reversing any rotational direction would be [0,-2,-3]?
I think that would be ok as an approximation, as long the time step is small.

#### A.T.

I have an angular momentum of [1,2,3]. In order to stop the rotation in 1 second, I'd apply a torque of [-1,-2,-3]. But, the torque vector I want to apply is [0,-2,-4]. Would I be able to simply compare components and determine that the force I want to apply without reversing any rotational direction would be [0,-2,-3]?
On a second though: it would be better to scale the other torque components accordingly so you don't change its direction. In the above case you would apply [0,-1.5,-3]

#### Bob S

Look up "center of percussion" on google.
http://en.wikipedia.org/wiki/Center_of_percussion
An impulse (application of a force x time) applied at a single point can stop the the angular motion of a rigid body, but it will result in a linear motion of the center of gravity.
Bob S

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