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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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2 answers
13 views

Would a homogeneous rod on a fulcrum oscillate or remain at rest after displacement?

If I take a homogeneous rod, put it on a fulcrum, push one side down in a controlled way and release very carefully won't the rod just stay at rest in that new position? ChatGPT says that it would ...
1 vote
1 answer
88 views

Mapping between generalized forces and external torque of a rigid body whose rotation is described by quaternion is not unique(?)

In this paper the mapping between generalized forces and external torques for a rigid body (when the rotation is described by a quaternion) is derived: $$\textit{F}_Q = 2\textbf{G}^TT'$$ where $\...
0 votes
0 answers
10 views

Modeling centrifugal distortion with an effective charge distribution

The hamiltonian of a rigid object with a totally symmetric moment of inertia (i.e. a "spherical top") will depend only on the magnitude of its angular momentum. If we allow the object to ...
1 vote
1 answer
53 views

Tendon excursion method application/alternative for joint represented by quaternion in biomechanics

I am building a biomechanical model that consists of spherical joints. I wanted to represent these spherical joints by quaternions. I am struggling to derive how the muscles contribute to the ...
0 votes
3 answers
151 views

What happens if we prevent gyroscope to precess?

If we apply some torque to spinning wheel in a vacuumed space in body frame y axis, wheel try to precess due to gyroscopic effect but it will be prevented by obstacles as seen from picture, what will ...
2 votes
1 answer
209 views

Non-Holonomic constraint in rigid body dynamics

I have solved many problems on Holonomic constraint using Lagrange multiplier method but I don't know how to tackle problems on non-Holonomic constraint. Can anyone help me with the following problem ...
0 votes
0 answers
16 views

Determining Equivalent Point Forces for a Rigid Body Given Net Force and Torque [closed]

Consider a rigid planar body subject to a force field, such as the gravitational interaction between polygons in a 3D space described in this question. Given: The net force acting on the rigid body ...
34 votes
13 answers
27k views

How can the contact point of a body rolling without slipping have zero velocity?

They say that for a rolling body, the velocity of the contact point is zero. I'm not getting this. How can it be zero when it's in continuous motion?
2 votes
2 answers
186 views

Is angular velocity about any point in a rigid body always the same?

Suppose I have a disc that is in translational as well as rotational motion. Question 1: If we talk about the angular velocity of the disc, about which point is this angular velocity measured? (I mean ...
2 votes
2 answers
94 views

Is it possible to reproduce tennis racket theorem instability with a gymbal under earth gravitational field?

The tennis racket theorem (whose effect is also known as Dzhanibekov effect), states that the rotational motion around the intermediate principal axis is not stable (that is, any small disturbance ...
1 vote
1 answer
44 views

Can the motion of a rigid body be decomposed into translational and rotational motion about ANY point?

My textbook mentions Chasles' theorem which asserts that " it is always possible to represent an arbitrary displacement of a rigid body by a translation of its center of mass plus a rotation ...
3 votes
4 answers
562 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?
2 votes
1 answer
644 views

Confusion regarding torque and calculating linear/angular acceleration of an object when a force is applied a distance from its center of mass?

From what I have read/learned about torque, it appears that it is derived based on the idea that applying a force farther from a point about which an object rotates increases the rotational force ...
2 votes
3 answers
244 views

Are the ideas of angular velocity, angular acceleration, angular momentum, torque, etc only helpful for rigid bodies?

For rigid bodies, all the particles can have different linear velocities but the same angular velocity, so it makes it convenient to talk about the angular velocity instead. From there, we get to ...
0 votes
2 answers
56 views

Rolling ball on a surface with friction

For a point particle moving on a surface under the infuluence of gravity, the equation of motion is very easy to write down - the force on the particle is simply the projection of its weight $mg\...
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3 answers
731 views

If the net external moment on a body about a point is zero

I was told that If net external moment of some forces is zero about a point, then the net external force passes through the point. I know it's not true in general, what was the special condition ...
2 votes
2 answers
59 views

Do off-centre forces create additional energy?

When a force is applied to a rigid body at its centre of mass, it accelerates. Over time, that acceleration becomes velocity, which gives the body a certain amount of kinetic energy. However, if that ...
0 votes
1 answer
326 views

What is the moment acceleration of the center of mass for a rigid body under an external force

As shown in the following, a rigid body experiences an external force $\overrightarrow{F}$ away from its center of mass C: The rigid body is assumed to be free in space, experiencing no other force. ...
1 vote
1 answer
286 views

Why don't Euler's formulas for torque apply to this problem?

In my mechanics class we were assigned problem 9.44 from "Introduction to Classical Mechanics" by David Morin as homework. The problem and figure are below: Two wheels of mass $m$ and ...
2 votes
1 answer
341 views

Gyroscopic effect of a sphere

I am looking at: https://en.wikipedia.org/wiki/Euler%27s_equations_(rigid_body_dynamics) \begin{align} I_1\dot{\omega}_{1}+(I_3-I_2)\omega_2\omega_3 &= M_{1}\\ I_2\dot{\omega}_{2}+(I_1-I_3)\...
2 votes
1 answer
63 views

Motion of bowling ball

I'd like to model the motion of an asymmetric bowling ball thrown on a bowling lane. I know there's forward momentum and angular momentum that moment the ball is released, and there's of course ...
4 votes
3 answers
284 views

What is the physical significance of Moment of Ineria about a point vs Moment of Inertia about an axis. In which types of problems we use the former?

I know the mathematical formula of both about an axis and a point. But where exactly we use moment of Inertia about a point. For 2d objects like discs rotating in its own plane, the moment of Inertia ...
-1 votes
1 answer
61 views

Angular Velocity of 3D object rotating in space

For a sphere rotating about z axis, its angular velocity is rate of change of angle of a radius vector in xy plane with x axis or y axis. I understand this clearly. But consider a 3d body which is not ...
3 votes
2 answers
251 views

How to apply a screw motion for this case?

I'm completely new to the notion of a screw motion. As far as I know, it carries out the the rotation and translation simultaneously in comparison with the homogenous transformation matrix that ...
1 vote
1 answer
48 views

Why isnt the contact force between the rack and wheel 200N?

I was looking at this YouTube video 'Example 1' (from 4:17 timepoint) and wondering why the contact force F between the rack and wheel isn't also 200N? Isn't this constant force of 200N being ...
1 vote
1 answer
60 views

Question on rotational dynamics

My book states that it's convienient to apply torque equation $\tau=I \alpha$ on instantaneous axis of rotation and centre of mass. My question is: why it is so? And how can we apply torque equation ...
-1 votes
0 answers
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Torque about an axis for an object [duplicate]

Suppose I have an object-(a disc for example), it is rotating about all of its 3 principle axes with some angular velocities .Along with that, the principle axes are also rotating, giving an extra ...
0 votes
1 answer
353 views

Motion of a point on a rotating rigid body in three dimensions

Let $\mathbf{p}$ denote a point on a three-dimensional rotating rigid body, and consider a body-fixed frame of coordinates centered on $\mathbf{p}$ rotating with the body. Assume that the body is ...
0 votes
1 answer
247 views

Confusion regarding derivation of euler's equation

I'm having confusion regarding the derivation of Euler's equation for rigid bodies. Suppose I have an inertial frame $O$, and a rotating frame $O'$ fixed to the rotating body and the rotating frame ...
0 votes
1 answer
445 views

Confusion about angular momentum of rigid bodies

I know that angular momentum of a rigid body has a parallel and perpendicular component to the angular velocity. I also know that the perpendicular component is due to constraints that keep the axis ...
1 vote
2 answers
246 views

Rotation axis for angular momentum and torque formulae to be valid

My current understanding of angular momentum and torques are that they are both defined for an arbitrary point, $o$, (pick the point and calculate, different points can have different values) and the ...
1 vote
1 answer
74 views

Is the idea of a rigid body compatible with Newtonian mechanics?

It is known that rigid bodies cannot exist in the framework of special relativity by causality arguments. But recently I saw a video on YouTube that claims rigid bodies are not compatible with ...
1 vote
0 answers
27 views

Evolution of rigid body system using Impulse Based integration [closed]

I have been reading about physics engines, I have a reasonably OK understanding force based models and 6 dof integration. I'm still confused on how impulse based models work. What define the equations ...
0 votes
1 answer
178 views

How can precession produce a torque in the direction of precession when it has no angular momentum?

Updated question, also includes somewhat of an answer. To clarify the point about precession having no angular momentum, if the torque that induces precession is suddenly removed, the gyro suddenly ...
0 votes
1 answer
64 views

Can torques cause both transitional and rotatory motion?

Imagine a rod (a rigid body) 10 meters long that is freely floating in space without being attached at any point. Its mass is 12 kilograms and according to most sources I found, its moment of inertia ...
3 votes
6 answers
168 views

Why can't rotations in general be associated with vectors?

In my textbook, there's a question: A vector has both magnitude and direction. Does it mean that anything that has magnitude and direction is necessarily a vector? The rotation of a body can be ...
1 vote
2 answers
605 views

Gyroscope precession and Euler equations

I've been trying for so long to solve this problem, but the solution I have found isn't the one I expected. Basically, I have to solve Euler's equations for a gyroscope with a weigth at a distance d. ...
0 votes
2 answers
496 views

If torque is the driver of rotation, why doesn't more torque (rotational force) mean faster rotation?

I got confused about the car. In most places they said that for acceleration when we start we need more torque (which is consistent with the fact that the highest acceleration is in first gear). But ...
0 votes
1 answer
66 views

How to compute inertia tensor off the center of mass with geometric algebra?

I was reading Doran & Lasenby's Geometric Algebra for Physicists when I stumbled upon this, where $\mathbf{a}$ is a vector taken form the centre of mass. Returning to the definition of equation (...
0 votes
3 answers
936 views

Rotational kinetic energy of rigid bar

Consider a rigid bar (infinitely thin and with uniform mass density) of length $L$ with $x_1(t), x_2(t) \in \mathbb{R}^3$ each describing the positions of an endpoint of the bar in some fixed inertial ...
7 votes
2 answers
1k views

Why can any general motion of a rigid body be represented as translation + rotation about center of mass?

Why can any general motion of a rigid body be represented as translation + rotation about center of mass? I am beginning to read rotational dynamics and my textbook states this fact without proof. I ...
0 votes
4 answers
73 views

Difference between the case where net force is zero and when no force is acting

I read online that the difference between the two cases is that the body deforms, but what if the body is perfectly rigid would there be another way to diffrentiate between the two cases? if not then ...
0 votes
0 answers
19 views

Does the direction of an angular velocity vector always stays constant with no force involved [duplicate]

Are there cases where there is a rigid body that rotates somehow and the direction of the angular velocity vector changes in the lab system?
0 votes
2 answers
53 views

Is energy conserved on a ball sliding without friction?

If a ball is sliding without friction (down an inclined surface) is energy conserved? I can’t think of why it wouldn’t be, but my intuition on this stuff is really bad.
1 vote
3 answers
489 views

How to find angular velocity vector of a three dimensional rigid body given velocity of three non-collinear points on the same?

The position of a three-dimensional rigid body is completely defined by specifying position vectors of three non-collinear points on the body. Similarly, one can define the motion of the rigid body by ...
7 votes
5 answers
1k views

Energy conservation for a rolling rigid body

I came across this question where A solid cylindrical body of mass m and radius r rolls without slipping over a smooth inclined plane. Its initial velocity is v. What would be the maximum height ...
2 votes
1 answer
43 views

Torque at only two points of contact between a rope and a disk (rigid body dynamic)

In physics, particularly when dealing with rigid bodies, there's a common practice of calculating torque at only two points of contact between a rope and a rotating disk, typically at the extremes ...
0 votes
1 answer
52 views

Is this the correct way to integrate orientation given torque and inertia tensor?

I am trying to develop a 3D rigid body simulation in C++ in which I had some conceptual doubts on how to integrate for orientation given the total torque applied to a rigid body, and it's initial ...
2 votes
1 answer
53 views

Centripetal acceleration of centre of mass towards instantaneous axis of rotation (IAOR)

When an object purely rolls on a horizontal surface, the centre-of-mass moves in purely circular motion, with respect to the instantaneous axis of rotation (IAOR). So does the centre of mass have an ...
4 votes
1 answer
263 views

Spinning Wheel subjected to Gravitational Force

have a question about the dynamics of a suspended horizontally rotating wheel subjected to gravitational force like in following picture I took from here: At the beginning the wheel has an angular ...

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