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Questions tagged [rigid-body-dynamics]

The study of the movements of a collection of connected bodies subject to external forces in the absence of deformation. This tag should be used for questions on the analysis of 2D/3D dynamics of rigid bodies, do NOT use this tag because your question contains a rigid structure.

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442 views

Can angular momentum be affected by internal forces in a rigid body system?

This question is motivated by my interest in understanding the angular momentum and energy of a figure skater doing a stationary spin where they move their limbs away from and towards their body to ...
134 views

Discontinuities in the angular momentum field

In Goldstein's Classical Mechanics, in the chapter on Rigid Body Mechanics he establishes the fact that no matter what point you choose on the Rigid Body, the angular velocity remains the same. The ...
140 views

How to determine the equations of motion of a rigid body's center of mass from a constraint?

Picture a rigid square with one of its vertices attached to the end of a massless rigid rod whose other end is attached to a point fixed in space. The motion is restricted to the plane containing the ...
• 119
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Oscillating frequency of a perturbed arc on the ground

This problem happens to me today. The illustration below is quite self-explanatory. Assume that there is no sliding, only rolling. Given an initial tilt, the arc will oscillate around the equilibrium ...
• 151
109 views

Why are stationary rotations of a rigid body about the largest principal axis not Liapunov stable?

In Arnold's Mathematical Methods of Classical Mechanics, 2nd ed., p. 145, he considers a rigid body with no external torque rotating about a fixed point O. He shows that the stationary solutions of ...
• 160
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Ring Ascending a Step

Consider a thin circular ring of mass $m$, radius $r$ rolling without slipping with velocity $v$ towards a step of height $h$ $(<r)$. Assume no rebound and no slipping at the time of contact. What ...
• 141
102 views

Why did Einstein allow unphysical objects in his 1906 paper on $E=mc^2$?

In the first part of this paper, Einstein considers a "rigid cylinder", "massless cavity", as well as a "massless carrier mechanism" that is used to transport the massless cavity. These hypothetical ...
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What is the potential associated to a pure torque proportional to one of the principal axis of a particle?

I'm writing a code in molecular dynamics in which a particle is subject to a pure torque around one of its principal axis. E.g., if the particle has principle axis $\hat u$, $\hat v$, $\hat f$, all ...
115 views

How can I simulate a rigid bounced from a wall?

How can I simulate a rigid sword bounced from a wall and hit the ground(like in physical world)? I want to simulate a simple animation. The sword is controlled by a center/mass point.(Actually finally ...
• 101
610 views

Torque of Air Resistance on Ellipsoid

Imagine an non-rotating arbitrary free, rigid ellipsoid with in some arbitrary direction with velocity $\vec v$. Assume linear drag ($\vec F=KA\vec v$ for some constant K, where A is the cross section ...
• 1,134
104 views

Does a hinged body rotates over its centre of mass if seen from the frame of centre of mass?

I know that if an unhinged body have some constant net force and some net torque it will rotate about its centre of mass and translate at the same time. Does a rotating hinged body also rotates about ...
50 views

Why is the center of 'percussion' called so?

I came across this word Center of Percussion while reading SHM from Resnick Halliday Krane Vol. 1 and couldn't figure out why it is called so. Please help me in doing so.
165 views

Numerical integration for simulation of rigid body using euler parameters

I am trying to numerically integrate the following equation of motion and solve for $\boldsymbol\omega$ vector(3x1) : \textbf{M} = [I]\dot{\boldsymbol\omega} + \tilde{\boldsymbol\omega}[I]\...
333 views

How is the equation $\tau_z=I_{zz}\alpha$ be satisfied for rotation about $z-$axis with $\tau_z\neq 0$ but $\tau_x=\tau_y=0$?

Consider the rotational dynamics of a door. The door can rotate about a vertical axis passing through the hinges. Let us call it the $z-$axis so that $\vec{\omega}=\omega\hat{k}$. I want to consider ...
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94 views

Different torques on a single rigid body

Assume I have a rigid body, on which two different torques are applied on two different surface points. I can calculate body inertia at each of those points. Describe the torques to the frame ...
There is something that has been bugging me for a while. Suppose I have a mass $m$ attached to a rod of length $l=1$ and with no mass and that the axes that we choose are not the inertial axis. ...