Okay, lets say you have a long horizontal tube is attached to a pin that it can freely rotate about in one angular dimension, placed at its center of mass. Now lets say it has 3 accelerators, one placed on the center of mass, and the others placed oneach end of the tube, producing force in the direction perpendicular to the tube. if you activate the middle accelerator, and the rotating pin is securely fastened to something, nothing should happen. Now if either of the other accelerators are activated, they produce a torque about the pin, and cause the tube to rotate, as described by the formula: t = r * f * sin(theta) where t is the torque produced, r is the distance from the center of mass, f is the translational force created, and theta is the angle between the acceleration vector and the vector from the center of mass to the point of acceleration. In this case, it would be 90 degrees, (1/2 pi radians), thus the acceleration creates a fully effective torque. (sin 90 = 1) Now, this causes no translational acceleration, only angular, since the pin prevents any movement. Now, image that this rod were in space, with no pin. We know by logic that the center accelerator should not create a torque, thus it uses pure translational acceleration in the classical formula f = ma. what happens when the outter accelerators are activated though? I know that they should produce a torque, but what kind of translational acceleration do they provide? I cant seem to find any books that document this situation, and its been bugging me all day. A man said to the universe: "Sir I exist!" "However," replied the universe, "The fact has not created in me A sense of obligation."

F = ma

F = 0

in this case, since the two accelerators are exerting force in opposite directions.

Treat force and torque separately.

MSN

You may want to take a look at this:

Computer Animation: Algorithms and Techniques

It explains what your are asking about in chapter 5.3.

my biggest problem would have to be my inability to adequately explain things to other people, heh.

I''d be a really crappy teacher.

to illustrate what i need to know, i drew up a diagram:


in diagram A, accelerators 1 and 3 both produce a torque when operated independantly, and act against each other when run simultaneously.

B just shows a side view.

I need to know what kind of translational motion happens in diagram C, when only one end accelerator is activated, and there is no pin holding the rod in place.

I''ll check out that URL, thanks.

A man said to the universe:
"Sir I exist!"
"However," replied the universe,
"The fact has not created in me
A sense of obligation."

in space there is no friction, right? so doesnt that mean that the entire object would move in the opposite direction it was pushing. it would also depend on if the thruster was perpendicular to the rod. if it was, there would be no rotation, right?

- Moe -

No because there is still inertia even though there is no friction. A force applied in line with the object''s center of mass would cause purely translational acceleration, but if it was offset from the center of mass, like at the end of the rod, it would cause rotation as well as some translation. I think the amount of translation would depend on the ratio of the partial masses of the object on either side of the force.

Looking at diagram C, if the force was applied exactly on the right end of the object, it would rotate to the left and the center of mass would not move. If applied in the middle, all of the force would be applied to translation. If applied somewhere in between, then some of the force would become translation and some would become rotation. You probably need to know how much mass is towards the center versus how much is away from the center.

You have to calculate the amount of force from the accelerator that acts in each way
I''d tell you how, but I can''t remember.

-Mezz

I think you''ll find your answer here:
Chris Heckers articles on dynamics.

I believe that in the appendix of the second article a problem just like the one you''ve illustrated is discussed.

The definition of a center of mass simplifies the linear component of your object''s motion. You can sum all the forces applied to your object (reguardless of where they are applied) and treat them as one force applied at the center of mass (proof in those articles). Scale the total force by the mass of the object, and that''s your linear acceleration.

The distribution of mass over the body of the object is called the Inertia Tensor, and is used to scale the angular acceleration of the object as it is integrated into angular velocity. Once you''ve calculated the linear acceleration, you can sum the crossproducts of the force vectors and the vectors formed from the object''s center of mass to the point of application on the surface of the body. Then, apply the inertia tensor to that vector, and you have a vector with magnitude(the angular velocity). The vector component is the axis around which the object is rotating, the magnitude is the velocity with which it is rotating.

The articles can better describe how these various values can be calculated and integrated to find you''re object''s new orientation.

I hope I got all that right

- genovov

I don''t think you can decompose the problem into linear and angular components like that. If what genovov say is true, the rod would go hurtling away in space along a straight line, neatly revolving about its center of mass, which defies intuition. I would expect it instead to travel in a long spiral, with occasional epi-spirals thrown in as the bulk of the rod swung about the rocket. This is an extremely non-trivial problem. In regards to the link presented above, I have a lot (a lot!) of respect for anyone nuts enough to pursue mastering linear/rotational kinematics on his own, but this stuff is really hard! I want to major in Physics, and spend a lot of time with it, and I see no easy answer to this problem. Might the proverbial grain of salt be in order?

I don''t think you can decompose the problem into linear and angular components like that.

That''s how physics is generally done...linear and angular measurements can be expressed in terms of the other, but the only interesting (== useful) translations are those which make the problem simpler. Often, combinations are used, so long as what you are describing in angular terms is not accounted for in linear terms, and vice versa.


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Look behind you! A three-headed monkey!