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Torque to eular angles

Started by llvllatrix Oct 31, 2002 at 12:38 AM 4 replies 1k views
Original Post
llvllatrix
llvllatrix
How do you convert a torque ie moment of force or ratation or whatever to euler angles given a change in time. As far as i can tell there would have to be some analogy to mass - perhaps the mass sourrounding the axis of rotation. Then you could find rotational acceleration but then what? I think it would probably be angle around the plane of rotation based on the elasped time. From there you would have to find world angles but...im not sure. Anyone know how? And heres another question if you''re up to it: If i apply a force to an object, at some distance from it''s centre of mass, at an angle theta to the fulcrum, what component of that force would cause the object to translate?
Sneftel
Sneftel
Let's cross over from the realm of regular dynamics to the realm of circular dynamics.

OLD: f=ma
NEW: τ=Iα
where τ (pronounced "tau") is torque, I is the Moment of Inertia, and α (pronounced "alpha") is the angular acceleration, in radians per second squared. Moments of inertia are like mass, but for rotating things.

So all your physics equations that built off of f=ma can apply here, too.

Let's try another one.

OLD: x=0.5at^2+v0t+x0
NEW: θ=0.5αt^2+ω0t+θ0

think of θ (pronounced "theta") as angular displacement, and ω (pronounced "omega") as angular velocity. It still applies here!

That should get you started. Play around with it, and see if you have any other questions.

Don't listen to me. I've had too much coffee.

EDIT: oh, and the equation for torque caused by force is the dot product of the force and the displacement of the force from the fulcrum.

EDIT: followed Fruny's lead and made my greek letters better.

[edited by - sneftel on October 31, 2002 2:04:30 AM]
Fruny
Fruny
The equivalent of mass for rotation is the moment of inertia J. Look it up.

T = J dθ²/dt

Euler angles are inappropriate for this kind of problems.
Store the orientation of your object as a quaternion.

The force exerted on an object applies fully for translation regardless of the point of application. Only the torque changes.

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RPGman
RPGman
There is a complete thread about your last question. I started it ;-) Check it out the title is "torque and linear forces" I think.
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shurcool
shurcool
or you can read these series of great articles on rigid body dynamics by Chris Hecker, 2nd part being on exactly what you're looking for.

his website can be found here.

the article you need can be found here.

but i suggest you check out the rest of his physics page.

edit: sorry for double post. =\ can't fix it since it anony'ed the 1st one. =T

---
shurcool
wwdev

[edited by - shurcool on October 31, 2002 9:32:17 AM]

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