# Tagged Questions

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### Gauge formalism in rigid body mechanics

When doing calculations in rigid body mechanics, it is necessary to choose an origin to calculate torques and angular momenta. However, the underlying dynamics does not depend upon the choice of that ...
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### point-particle vs rigid-body [closed]

As pointed out here point-particle-based modeling can lead to very inaccurate predictions. Could you give an example where point-particle-based model describes reality accurately enough and one where ...
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### Solving for motion of rotating rod using only Newton's laws?

I have a question that's been bothering me for years. Given a rod of uniform mass distribution with total mass $M$ and length $L$ that lies on a horizontal table (with one end fixed to the table ...
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### Is having full information about the resonances of a rigid body equivalent to having full information about its material parameters?

Lets say I have a mechanical system whose mechanical resonances (mode shape and frequency) I can measure with perfect accuracy. Is this theoretically equivalent to knowing the materials parameters, ...
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### Inertia matrix of a rod rotating about an axis [closed]

I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, ...
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### Eulerian Angles — Why three rotations can transform fixed frame into body frame?

"In general, if we restrict ourselves to rotations about one of the Cartesian axes, three successive rotations are required to transform the fixed frame into the body frame" The origin of our fixed ...
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### When does the angular momentum point in a different direction from the angular velocity?

I read this somewhere: $$\mathbf{L} = \tilde{\mathbf{I}}\mathbf{\omega}$$ In general, the angular momentum vector, $\mathbf{L}$, obtained from Equation above, points in a different direction to the ...
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### Push a box in a plane with friction. How to deal with the rotation?

Suppose I have a box (say, length-1m, width-1m, height-0.5m) on the plane with friction. I can apply a horizontal force in on the surface of the box. If the force doesn't pass through the center of ...
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### Rigid bodies - the wheel

As I've been taught lately in my mechanics course: the wheel has a unique property: at every moment of motion, the touching point between the wheel and the ground is not in movement and ...
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### What is a bilateral constraint?

In the realm of mechanics/rigid body dynamics, can anyone tell me what a bilateral constraint is? Can't seem to find any information on the exact definition, just uses of it such as "considering only ...
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### Is there an equivalent of a scalar potential for torques?

For a given scalar potential $V$, it is known that the corresponding force field $\mathbf{F}$ can be computed from $$\mathbf{F} = -\nabla V$$ Suppose a rigid body is placed inside this ...
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### How to combine these equations of constraint?

I want to model a nonholonomic system of an arbitrary rotating disk in 3D, which rolls without slipping, and doesn't have to stay vertical. (think spinning a penny on the table) I want to use the ...
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### Intuitive explanation for why same force applied farther from a hinge causes larger angular acceleration than if applied closer?

A standard example of a problem involving torque is opening a door - the same force F applied far from the hinge causes a larger angular acceleration than if applied close to the hinge. I always had ...
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