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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Independent coordinates of a rigid body

This is a quote from Classical mechanics by Goldstein: "To fix a point in a rigid body, it is not necessary to specify its distances to all other points in the body ; we need only state the ...
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Who is the person behind the so-called “Boure's Law”?

When I was in college, specifically in Rigid Body Kinematics, I was taught that Boure's law or formula, which looks something along these lines: $$\left(\frac{\mathrm{d}\boldsymbol{\omega}}{\mathrm{d} ...
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Conceptual question about rotating cube about unstable equilibrium point

Let's say we have a cube of mass $m$ and side 2a is held poised on one of its edges on a horizontal surface. It is released from this position and allowed to tip. Here we have two cases : Case 1 : the ...
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Newton-Euler inverse dynamics

I am trying to understand Newton-Euler inverse dynamics algorithm from Northwestern Modern Robotics course. Think everything is clear except for one issue. Here is a 5 minutes brief video lecture ...
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Find a reference frame for a straight line rigid system

A body reference frame is a reference frame moving with a rigid body. So any rigid system has at least two points $P$ and $Q$ and these are such that $$ \vec{QP}\,\cdot\,\vec{QP}=\text{constant} $$ by ...
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Understanding Euler's Rotation equation for rigid bodies (Frames Of Reference)

$$ \tau_b=I_n\dot\omega_b+\omega_b\times I_b\omega_b $$ Now in the above is Euler's famous rigid body rotation equation, in the body frame of reference ..... this does not make sense to me. How can a ...
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Why does a body rotate faster if force is applied away from the pivot?

Why does a body rotate faster if force is applied away from the pivot? I need an intuitive answer to this. Like why does a door rotate slower if I push at it closer to its hinge, or faster if I push ...
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Relative angular velocity of rigid bodies [closed]

If all the points in a rigid body have same angular velocity (say, $\vec{\omega}$), then why is angular velocity of point $A$ in the body w.r.t. point $B$ in the body is still $\vec{\omega}$ and not $\...
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Collisions with Spheres (with Different radii) on a plane

How do you calculate the new velocity of the spheres after a collision when the spheres have different radii? I thought you could just decompose the horizontal velocities and use the standard ...
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Euler's equation for rigid body rotation applied to inertia frame, with body frame both rotated and translated with respect to the world frame [duplicate]

The Euler equation is usually expressed in a local body frame: $$ τ_b=I_b \dot{\vec \omega}_b + \vec \omega_b \times I_b \vec \omega_b $$ Where the subscript $b$ indicates that the respective term is ...
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A question about rotation around the center of mass

Consider a body which is static with respect to an inertial reference frame. If I apply an impulse $\vec{F} dt$ with known magnitude and direction at a point $P$ which is different than the center of ...
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Can you intuitively explain the decreasing time-period of oscillation with increasing pendulum length in some cases?

Consider a rigid body suspended about an axis of rotation which, in general does not pass through it's center of mass (COM) and has a moment of inertia (MOI) $0 < I_{axis}$ about that axis. Let $...
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Objects falling from table

It is an everyday experience: You have placed an object a tiny little bit too much over the edge of a table and it falls down. This is the case when the center of gravity is above the floor and not ...
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Time stepping in Rigid Body Dynamics

When simulating the interaction of 3d rigid bodies, how do you decide what object you advance the state on first? If you advance all bodies at the same time there will be intersection/constraint ...
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Rigid Body Motion and defining $\vec{L}$ and $\vec{\omega}$

This is a study question I have been struggling with, I would appreciate help defining initial vectors to start the question. We consider a thin circle shaped disk (mass m, radius R). The moments of ...
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1answer
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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)\...
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49 views

Motion of a rigid body on application of constant force perpendicular to a point which is not the center of mass?

Consider a rod which has a uniform mass distribution which is free to move in space. Now, it is known that if an impulse (perpendicular to rod) is applied which does not pass through the center of ...
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4answers
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Spinning ball colliding inclined plane [closed]

[![Solution][2]][2] "A solid uniform ball of mass M and radius R collides elastically with a rough fixed with a rough inclined surface as shown. Velocity and angular velocity of the ball just ...
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1answer
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Applying torque to rigid body on a fixed axel?

Suppose I have a torque $\tau \in \mathbb{R}^3$ on a rigid body, about its center of gravity, where the direction of $\tau$ is the axis of the torque and the magnitude of $\tau$ is the strength of the ...
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How to calculate forced precession torque in a gyroscope?

If I speed up the precession rate of a gyroscope the gyroscope responds with a counter torque, what's the equation for that torque?
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Conceptual question about instantaneous centers

In the following six bar linkage instantaneous center 2,6 ($P_{2,6}$ on the diagram) and slider D have equal velocity. But instantaneous centers have zero velocity and the velocity of other points on ...
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Estimation of greatest speed in a polyhedron

in order to control velocities in a three dimensional volume, I look for a proof or a proof idea for the following assumption: Given a non-empty solid polyhedron in 3D, all points inside this set ...
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How can a rigid body's weight do work on it to make it rotate?

Consider a cylinder that rolls without sliding on an inclined plane. If it's placed at the top of the plane, with its center of mass at a height $h$ from the bottom, it will have a potential energy $...
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Inertia tensor formula for point masses in rigid assembly?

Suppose I have $N$ 1kg point masses in a massless rigid assembly such that the center of mass of the assembly is at the origin and point mass i is at $(x_i, y_i, z_i)$. The inertia tensor of the ...
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1answer
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Precession - why decompose to angular momentum component?

I always see it is conventional (in Landau-Lifshitz for example) to decompose the angular velocity vector to 2 components: axis of symmetry and angular momentum vector, and then define the angular ...
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How weighing balance works and can balance itself?

i am new in this community and i was not able to answer in a similar post "how does a weighing balance that has 2 identical mass on both sides is capable of balancing after being tilted". i ...
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Can the Newton - Euler equations be used to model a rigid body attached on several springs?

imagine a three dimensional rigid body with known Moment of Inertia (at the center of mass) $I_{\text{cm}}$ which is suspended by several springs at different points on the surface of the body. The ...
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1answer
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Are mass and moment of inertia sufficient to describe the motion of a rigid body?

Context: how to build a VR controller such that swinging it is indistinguishable from swinging a sword. Is it enough that the controller matches the sword in mass and moment of inertia about the ...
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Finding relation between Torque and rate of change of Angular momentum , different approaches are giving different results [closed]

All the vectors here are measured in the inertial frame of reference $I$ . Notation used : $O$(origin) is a fixed point in $I$ . $C$ is the center of mass of the rigid body that I am considering and $...
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1answer
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Question Regarding the conservation of momentum in an inelastic collision of two rods

I am tasked with solving this question but am facing some intuition difficulty. consider this system: The empty circle signifies a nail that is stuck in the wall. I am unsure if there is conversion ...
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1answer
56 views

Proof of work-energy theorem for a rigid body

Could anyone show me a way to derive the work energy theorem for a rigid body whose motion is along a fixed axis ( such as of a cylinder rolling on a plane) which states that states that $W=\frac{1}{2}...
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Can a high density of particles simulate fluid dynamics?

There are different ways to simulate fluids, some involve numerical solutions to PDEs. I was wondering if these PDE formulations can be thought of as an a infinite limit of a collection of particles? ...
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116 views

Inconsistency in work-energy principle for a spinning body set down to roll [closed]

A spinning solid cylinder spinning with $\omega_0$ is put smoothly on a plane. It will skid until it begins to roll with $\omega$ Argument 1 We know that, work done by all the forces assumed to act ...
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Work and mechanical energy relationship for a rigid body

For a single particle in a conservative field, I know that the work done by an external non conservative force $W_n=\Delta M$ where $\Delta M$ is the total mechanical energy. Is the same true for an ...
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99 views

SHM of a rigid body

In the analysis of SHM of a point sized bob oscillating with small angular displacement we can analyse the SHM in both linear and angular terms and arrive at the same answer and this should be true ...
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Angular Momentum and Kinetic Energy of a Rigid Body

The inertial tensor of a homogeneous rectangular sheet of mass m with sides of respective length a and b and negligible thickness is: $$I = \frac{m}{12}\begin{bmatrix}b^2 & 0 &0 \\ 0 & a^2&...
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2answers
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When is static friction dissipative and when it is non-dissipative?

In some cases, like in pure rolling, static friction is non-dissipative in nature. So, how can we identify when is static friction dissipative or non-disspative?
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Minimum gyro speed to yield force precession

Does anyone know what the minimum speed of a gyro to make it so a force at 0deg will yield a movement at 90deg? or even better, what the angle is wrt speed? see http://www.copters.com/aero/gyro.html ...
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A general question about precession

Does precession (of a top for example) occur only whenever the angular velocity vector is not parallel to a principal axis? I have yet found any clear definition of precession and when it is defined ...
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1answer
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Why cannot this be solved using centre of mass [closed]

One end of a uniform rod of mass m and length l is supported by a frictionless hinge which can withstand a tension of (1.75mg). the rod is free to rotate in a vertical plane. To what maximum angle ...
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Is it correct to choose Rod's COM as origin of an inertial cordinate system?

I was trying to apply Chasles' theorem to the question attached below. To study the Dynamics I need to apply Chasles' theorem to convert the motion into a combination of rotation about the center of ...
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How is length contraction on rigid bodies possible in special relativity since definition of rigid body states they are not deformable?

This is more like a conceptual question. We define rigid bodies as solid bodies with zero or almost zero deformation (meaning the deformation should be negligible). So no distance between two points ...
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If a body is lying on a frictionless surface, and we give it an impulse, will it start rotating about its center of mass?

If not, about what point will it rotate? If we want to know about what point an object will rotate in questions like these, how do we figure it out?
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Why is angular momentum conserved if we keep a ball on rough surface with only translational velocity after it attains pure rolling motion

Assume a ball to be kept on a rough surface with intial translational velocity V and no rotation. After some time it aquires pure rolling. It is acted upon by an external torque due to friction still ...
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241 views

General plane motion and freely floating rigid body

Consider a rigid rectangular plate of length $l$, width $w$ and thickness $t$ which is at rest and is floating freely in space (no gravity). The center of the plate is at $O_L$ with respect to global ...
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If you apply a force against a fixed body (no motion) for a certain period time, is the resulting force time integral an impulse?

Say I'm 100 kg and hanging off a pullup bar for 10s. The force-time integral over that period would be FTI = 9.81 kNs But do I apply an impulse? According to the definition on Wikipedia, I would say ...
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Accelerometer (on a rigid-body) readings, knowing its position and attitude in an inertial frame

Good morning, I'm trying to simulate a rigid body with some accelerometers attached to it. The aim is to simulate accelerometers readings that will be later fed into a Kalman Filter (after being added ...
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2answers
30 views

Friction on a rod resting against a rough horizontal rail? [closed]

In which direction does friction act on a rod leaning on a rough horizontal rail, where the normal force is perpendicular to the rod and the rod has its bottom end on a smooth horizontal floor with ...
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1answer
47 views

Adiabatic invariants for rigid bodies

I Landau & Lifshitz I mechanics introduces adiabatic through Hamiltonian that is dependent on some slowly changing parameter $\lambda$. After some derivation they got $$I=\frac{1}{2\pi}\oint pdq=...
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How to calculate the derivative of the angular momentum vector $ d\vec L = d(\hat I \vec \omega)?$

My last question, but also the most important one How to calculate the derivative of the angular momentum vector? $$ d\vec L = d(\hat I \vec \omega)$$ I'm especially interested in derivative tensor to ...

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