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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4answers
348 views

Instant centre of rotation for two connected gears

The two gears are have the angular velocities $\omega_1$ and $\omega_2$ respectively with respect to $Oxyz$. The task is to determine the angular velocity $\boldsymbol{\omega}$ of the arm ...
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2answers
49 views

Does Angular Momentum change what I change Center Of Mass?

So recently I've noticed some discrepancies in my physics simulation, and these occur when I add/remove particles from a rigid body. Strange things like things flying to the sky constantly occur, and ...
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2answers
212 views

Why falling camera/objects rotate and then stabilize?

I was going to ask something very similar to this question (which hasn't been answered). Basically a camera fell from an airplane and it began to rotate (maybe because initially it was put in rotation ...
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1answer
356 views

How do I treat the Lagrangian in the case of a rigid body?

Here's Exercise 1.11 from Goldstein's Classical Mechanics 3rd edition (the first one after having derived the Lagrangian basically): Exercise 1.11: Consider a uniform thin disk that rolls without ...
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1answer
65 views

Analysis of motion of a body moving on a string?

I was wondering about something I observed yesterday. To give some background, one of my hobbies is slacklining. This is essentially like tight-rope walking but with a one inch piece of (in this case ...
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1answer
43 views

Rotational work and forces such as static friction or ropes tension

I'm confused about the rotational work, defined as $W=\int_{\theta_1}^{\theta_2} \tau_z d \theta $ Where $\tau_z$ is the component of the torque parallel to the axis of rotation $z$. Consider a ...
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1answer
50 views

'Eulerian' description of a rigid body submerged in fluid

In this paper, equations of rigid body motion (eq 4 and 5 in the paper) are written in Eulerian form (eq 12 in the paper). The rigid body is submerged in a viscous incompressible fluid. ...
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1answer
58 views

Degrees of Freedom for an Asymmetric top

How many degrees of freedom does an asymmetric top have if it is rotating about a fixed point?What are the generalised coordinates used then?
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1answer
394 views

Rigid body problem in 2d

I have some questions about this exercise: In an horizontal plane, a $OA$ bar with mass $m$ and length $a$ moves, with another bar $AB$ (same mass, double length) attached in the point A. In the ...
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1answer
26 views

Principal axis of inertia parallel to the ones passing through the center of mass

Consider a rigid body and the (at least) three axes of inertia passing through its center of mass. Will any other axis not passing through the center of mass but parallel to one of the principal axes ...
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1answer
16 views

Calculation of support reaction in rigid body rotation and collisions

I can't understand the logic behind the calculation of torques exerted by supports in rigid body motion, especially rotation. The equation of angular momentum is ...
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1answer
20 views

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 ...
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1answer
29 views

Instantaneous axis of rotation of a rigid body

For the description of rigid body motion, any point $O$ of the rigid body could be taken as reference, since the velocity of a generic point $P$ can be written in function of the angular velocity ...
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1answer
29 views

Which force acts as centripetal force on gyroscope?

I think I have understood gyroscope in terms of angular momentum and how the torque of gravitational force moves it the way it does. Also I understand the direction in which it would move: What ...
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1answer
40 views

Rigid bodies and inelastic collision

If two rigid bodies collide - how the collision can be inelastic? where the energy goes? If the energy transffered to heat, doesn't it contradict that the bodies are rigid?
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1answer
71 views

Why do we need theorems like **Parallel Axis Theorem**

In rigid body pure rotation, quantities like $\omega, \tau, L, I, r_i$ (symbol with usual meaning) are axis dependent. Assume rigid body to be sphere rotating about the axis passing trough the center. ...
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1answer
67 views

Transform velocities from one frame to an other within a rigid body

I come from non-physics background but just came to face the following problem. I have a rigid body with two attached frames of reference A and A'. I know: the rotation and translation between A ...
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1answer
14 views

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 ...
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0answers
88 views

Where this relation for general non rigid motion comes from?

In Goldstein's Classical Mechanics book in the chapter about the dynamics of rigid bodies the equation $$\dfrac{dL_i}{dt}+\epsilon_{ijk}\omega_jL_k = N_i$$ is presented. Now, in one exercise, we are ...
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0answers
173 views

What kind of shape has the lowest flutter wind speed?

What kind of shape has the lowest flutter wind speed and is the most unstable? I mean for rigid body. Thanks Yes, I know many factors affect the flutter in a MSD system (for rigid body), however ...
2
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0answers
70 views

Precession of angular momentum vector

I'm studying Classical Mechanics on Goldstein's book, so I'm using his terminology and notation. First I'll explain where the question comes from: consider a heavy symmetrical top and consider the ...
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0answers
44 views

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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0answers
37 views

What causing the axis of rotation of a bowling ball to change

A bowler throw a bowling ball with an initial velocity and initial rotation. Let the initial velocity vector be parallel to the y-axis. Now, the ball is rotating about an axis, call that the axis of ...
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0answers
77 views

Rotational dynamics equation for a variable mass system?

I'm searching for the formulation of Euler's rigid body dynamics in the case of a variable mass system. I'm reading the book Mechanics of Flight by Warren F. Phillips (2nd edition) and unfortunately ...
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0answers
119 views

Contact between two rigid bodies. How does contact force is distributed in the contact surface?

We have a rigid body with some scalar function of vector argument, which describe density of body at concrete point in space. The body lie on the table in the stable state, elements of it doesn't ...
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0answers
86 views

Rigid body translation and the moment about a point

ok the statement of the moments , beside the fourth car image How there is a moment about the point A although there is only translational motion , is not the car only moving and not rotating ? ...
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0answers
67 views

Terrestrial Space Elevator Construction - Plausability

Framework If there was a cable constructed at the equator about the circumference of the Earth, and if this cable had sufficient strength to remain intact while erect, call this tensile strength T. ...
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0answers
61 views

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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0answers
152 views

A rigid rotating rod that breaks in two pieces

Suppose we have a rigid rod of lenght $L$ and homegenous mass density. One of its extreme points, say $P$, is fixed so that the rod can rotate around the axis passing in it. Initially the rod is held ...
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0answers
63 views

Loaded die problem

A loaded die has an uneven mass density distribution. A given die is constructed from a square pyramid of material with mass density $\rho_1$ whose bsase lays on the face marked "1",with the rest of ...
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0answers
73 views

Euler's equations (rotating frames)

I'm trying to understand the Euler's equations and I'm having problems with rotating frames and on which specific frame is each quantity measured. On the equation $$ ...
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0answers
18 views

Locus of a point on Euler's disk

I have been struggling to find how a point on the surface of Euler's disk varies with time in $x$ ,$y$ and $z$ coordinates. The disk has a radius $R$ and a thickness say $T$. It originally makes an ...
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0answers
17 views

Distribution of contact force

Say we have a body resting on a flat surface. The force of gravity acts through the center of mass. The normal force is equal in size and in oposite direction. Since the body is in contact with ...
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0answers
14 views

Angular acceleration of rigid body due to a torque

For the rotation of a rigid body about a fixed axis $z$ the following holds. $$ \vec{τ_z}= \frac{d \vec{L_z}} {dt} =I_z \vec{α} \tag{1}$$ Where $ \vec{τ_z}$ is the component parallel to the axis ...
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34 views

Rigid body rotation about fixed axis with angular velocity not constant in magnitude

I'm trying to understand the properties of angular momentum in the rotation of a rigid body around a fixed axis $z$, when the angular momentum $\vec{L}$ is not parallel to the angular velocity ...
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0answers
76 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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0answers
21 views

Relative velocity of the center of mass in a rotating coordinate system

Say I have a rigid body in space. Let k be a stationary coordinate system, K a coordinate system rotating together with the rigid body, so the transformation $B:k \rightarrow K$ it's just a simple ...
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0answers
11 views

Understanding the inertia matrix of a tilted ellipse

I would like to control the rotation of an ellipse which is tilted by 45° with respect to the rotation axis, and I need to calculate the inertia of the load on the shaft. To be clear, on this figure I ...
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0answers
31 views

Rotating disk moving on a circular path

A uniform disk with radius $R$ and mass $M$ is in earth's gravitational field (i.e $\vec{g}$). A point $A$ on the perimeter of the disk is attached to a circular path with radius $L$, and the disk is ...
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0answers
41 views

Tangential Velocity of a Rotating Rod

I have the following question which has given rise to a doubt. Question: One end of a rod of uniform density is attached to the ceiling in such a way that the rod can swing about freely with no ...
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0answers
43 views

What is required for a time-varying moment of inertia matrix?

Let me preface this question by stating that I am familiar with euler's equations for rigid body dynamics, torque and angular momentum. Despite the math, I'm still a little fuzzy about certain ...
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0answers
20 views

Equation of motion for rigid T-shaped object

Suppose I have a rigid T-shaped object, that is described by three points $A,B$ and $C$. $A$ and $B$ describe the corners of the "top" of the "T", lets say these have coordinates in 3D of $r_A = ...
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0answers
22 views

Polygon with moving/rotating vertices (or chained line segments)

Suppose we have a polygon, where vertices are point masses, and rods joining them are massless. Now, we pull one of the vertices, what equations govern the motion. How about if instead of a polygon we ...
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0answers
26 views

Rotational Velocity

I would like to calculate rotational velocity from Global(fixed frame of reference) in local (moving frame of reference). How to do that? i know the relationship between global and local frame of ...
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0answers
50 views

When a force applies to a rigid body at point, then does every part of the body experience the same kind of force?

Suppose that a rigid body is static under the action of several forces that are applied at different part of the body. Then is it true that if one divides the body into small pieces, then each piece ...
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0answers
26 views

How to prove the relation between the rate of change of a vector in space coordinate and in body coordinate?

I'm learning Goldstein's classical mechanics, and in chapter 4.9 he prove such an operator equation $(\frac{d}{dt})_s=(\frac{d}{dt})_r+\omega \times$ In the proof, he takes the space and body axes as ...
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0answers
447 views

Calculating Inertia Tensor with Parallel Axis Theorem

Say you have a solid you are approximating as n point masses at different points in a 3D space. Each point mass has a mass of 1. The origin is not the center of mass. All the points have location ...
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0answers
98 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 ...
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0answers
273 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 ...