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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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(A general obs.) A cylinder is placed on a plane which is performing shm as $x=acos\omega(t)$ [on hold]

A cylinder is placed on a plane which is performing shm as $x=a \cos \omega t$ (or totally stating it as) If so how can we write general equation of torque acting on the cylinder as the Plane is ...
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1answer
45 views

Addition theorem for angular velocity --> “addition theorem for angles”

I'm wondering if it is possible to go from the addition theorem for angular velocity to the "addition theorem for angles". For example (I used the same notations of Wiki): $${^N\!\omega^B} = {^N\!\...
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0answers
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Condition for balance of rigid body

I'm learning this subject right now and I didn't understand this problem from the book, also for you, the reader I mark: $$\textbf{N} = momentum\;N = normal\;force$$ The problem is: A box with the ...
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2answers
55 views

Is rigid body mechanics included in classical mechanics?

Can rigid body mechanics be derived from Newtonian, Lagrangian or any other formulation of classical mechanics? Or do we need some extra axioms or laws?
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1answer
42 views

Is a reference frame fixed (without rotation) on a precessing gyroscope an inertial frame of reference?

Let's say we put a human in a closed chamber which is going around a certain point at distance d from its center of mass at some angular velocity w. The centrifugal force on a human will be w squared ...
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5answers
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How can friction do no work in case of pure rolling?

I have read various answers , on PSE and elsewhere , and most of them explain that the point of contact of the rolling object undergoes 0 instantaneous displacement in the direction of friction, I ...
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0answers
37 views

Time derivative in rotating frame

In Goldstein (2ed) sec 4.9 - Rate of change of a vector, why does he say that the instantaneous angular velocity $\omega$ is not a derivative of any vector? $$ (d\textbf{G})_{space} = (d\textbf{G}...
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An energy/model based controller to minimize overshoot and response time of a mass spring system

Consider a very simple system: $$m a + k x = F \, , \tag{1}$$ where $m$ is mass, $a = \ddot{x}$ is acceleration, $k$ is the spring's elasticity, $x$ is position of the mass and $F$ is the force from ...
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1answer
40 views

Euler's equation of the rigid body's dynamics - Vector form with rigid body's angular acceleration

I have the following Euler's equations (9.23) ($\omega $ is the rigid body's angular velocity, $\Omega$ is the angular velocity of the reference frame whose origin is fixed on the rigid body and whose ...
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0answers
49 views

Rigid Body Equations in terms of Body Coordinates by Hamilton's Principle

I sought-for the equations of motion of an unrestrained rigid body. The equations of motion are readily available in the literature, but my concern is to derive them by Hamilton's principle. ...
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Rigid (planar) Multibody system: How are these equations of motion linked to the model?

This a second question I have on the same subject as my previous question, so I will make a link here (Motion equations for Woodpecker toy (multibody system)) to that question (and a link from that ...
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1answer
49 views

Cube tumbling over

When a moving cube hits a low step (the step is perpendicular to its velocity) and tumbles over, is its angular momentum conserved? It is implied that it is so, but certainly gravity produces a torque ...
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3answers
42 views

Position of center of mass/gravity that ensures balance

I have got this problem asking where should the center of mass be positioned in the Y axis to ensure that the "system/body" is stable. Picture: Let the table be y=0 The answer is that the center of ...
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0answers
28 views

How to determine the distance of slipping in a toppling body?

A body of known mass is connected to the top of a light rod which perpendicular to the floor. As the body starts to fall, the base of the rod slips before the edge of the mass comes in contact with ...
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1answer
52 views

Mathematical segmentation of an accelerating body and the resultant torques

My question is inspired by problems of the following kind: To solve such problems, what one essentially does is mathematically 'segment' the rod/body at a distance x from the pivot, and then write ...
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2answers
86 views

Mechanics: angular momentum of disk

I am studying mechanical engineering and I've got a problem with the angular momentum of objects that have a rotation which is rather complex to describe like the following: The shaft rotates around ...
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1answer
49 views

Torques in Euler equation

The Euler equation is given by $$\mathbf I\dot{\boldsymbol \omega}+\boldsymbol\omega\times \mathbf I\boldsymbol\omega= \mathbf M.$$ Also see here. It explains that The expressions for the torque in ...
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1answer
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Lagrangian of a Heavy Symmetrical Top - Inertial or Non-inertial Frame?

I'm having some confusion with the analysis of a symmetrical top (specifically, a heavy top, but this is not very important for the question). Following Landau and Lifshitz's Mechanics, on page 110 ...
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1answer
45 views

Kinetic energy of a gyroscope toy [closed]

Why the energy only has rotational part $\frac{1}{2}I_1\omega_1^2+\frac{1}{2}I_2\omega_2^2+\frac{1}{2}I_3\omega_3^2$? The center of mass also moves in general.
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1answer
37 views

Deriving velocity in rolling without slipping in another approach

I want to derive the velocity of a point P on a surface of a cylinder rolling on a flat plane, by considering the rolling as instantaneous rotation with repect to the contact edge line E of the ...
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1answer
44 views

What happens when you try to turn a gyroscope with high torque?

I apologize for my lack of basic understanding of gyro-physics, I tried looking up internet, but couldn't find any answer for this particular question. I have been told that if I apply torque to the ...
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0answers
69 views

Why does conservation of energy appear to be violated? [closed]

I am currently working on a rigid body simulator. Before getting proper collision and rotations working, I decided to simulate the collision of spheres as axis-aligned objects. The simulation works ...
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0answers
31 views

Basic doubts about dynamics of a rod [closed]

I have few doubts in the given solution. It says there is no force along the plane but $mgcos\alpha$ is acting along the plane ? As given, $A$ is used as orgin. Then how come x-co-ordinate of $G$ is ...
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1answer
107 views

Using Euler equations to solve for torque

I am trying to solve the torque needed to rotate a rectangular plate of sides $a$ and $b$, about a diagonal with constant angular velocity $\omega$. Euler equations are given by, $$ I_1\dot{\omega}...
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3answers
76 views

How many moment of inertia about center of mass exist?

So imagine we have a rigid body and we want to find the moment of inertia about center of mass . Doesnt exist infinite axis that pass trough center of mass therefore infinte moment of inertia? Do they ...
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0answers
249 views

Deriving moment of inertia of a solid sphere [closed]

I have been trying to calculate it on my own, but the answer I get is different to the one I can find everywhere else, so I have to be wrong. My attempt was a very straightforward one. I used ...
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2answers
150 views

How to choose the perpendicular axis?

This site https://en.wikipedia.org/wiki/Perpendicular_axis_theorem says: Define perpendicular axes $x$, $y$, and $z$ (which meet at origin $O$) so that the body lies in the $xy$-plane, and the $z$-...
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1answer
87 views

Integrating rigid body equations for a game engine simulation

I'm a mechanical engineer who's trying to implement a physics engine for a 3D game simulation, so I apologize for being incorrect or simply ignorant of some aspects of computation. I'm implementing ...
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1answer
72 views

Relation between rotation vector derivative and angular velocity when the rotation angle is constant

$\def\va{\vec{\alpha}} \def\vw{\vec{\omega}} \def\vn{\vec{n}}$Let $\va(t)$ be a rotation vector such that its direction is the rotational axis and its length $\alpha=|\va|$ is the angle describing the ...
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1answer
46 views

Angular acceleration in rigid body dynamics

I'm a little confused. In rigid body dynamics, could we write $\alpha = \frac{a}{r}$ everywhere in combined translational and rotational motion? If not, then where we could write it?
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2answers
54 views

How does the COM of a rigid body always move as if only external forces influence it?

There's this example in my physics textbook: It seems to suggest that the resultant of all external forces acting on a body tells you how the COM of the body is going to move. Now, I understand the ...
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1answer
139 views

Is torque always equal to the derivative of potential energy with respect to rotation angle?

For any three-dimensional rigid body, the applied torque on that body is defined as: $\vec{\tau} = \vec{r} \times \vec{F}$ where $\vec{F}$ is the applied force on the object (i.e. $-\vec{\nabla} U$) ...
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3answers
117 views

Is it possible to understand the Gyroscope Effect Intuitively?

A stationary wheel, with its axis tied only at one end, falls down, but a rotating wheel, with its axis tied only at one end, doesn't fall down. The explanation given everywhere is by the ...
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1answer
162 views

The Euler-Lagrange equations for rigid body rotation [duplicate]

The equations of motion for rigid body rotation are: $I\,\dot{\vec{\omega}}+\vec{\omega}\times I\,\vec{\omega}=\vec{\tau}$ How i can calculate this equations using Lagrangian method ? If i use $...
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0answers
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Coin spinning on smooth table [closed]

A coin radius $r$ spins on a smooth table with its plane at a small angle $\theta$ to the horizontal. Show that the head on the coin, viewed from above, appears to rotate with angular velocity $\sqrt{(...
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1answer
43 views

In which scenarios is the derivative of mass moment of inertia ignored and taken into consideration for rigid bodies?

When taking the time derivative of Angular Momentum The first two terms represent the relative rate of change with respect to the coordinate system used. Most sources I have been reading state that ...
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2answers
243 views

What is the difference between precession and spin angles?

I was recently introduced to Euler Angles in a Dynamics course, but I am confused on the difference between precession and spin angles. Both precession and spin consist in rotating a coordinate system ...
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2answers
266 views

Degree of freedom in Lagrange's formalism

Degrees of freedom $=3K-N$ where $K$ is number of particles and $N$ is number of constraints. How to find the number of degrees of freedom for a rigid body which has both translation and rotation, ...
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1answer
45 views

Equivalent inertia at spherical joint in multibody tree

Consider a tree system of rigid bodies and spherical joints. Starting at an outermost body, I'd like to calculate its equivalent mass (which I'm guessing would be an inertial tensor or something) at ...
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2answers
60 views

Why does the sphere not roll?

It says in the first case that the sphere never rolls. Is it possible for a sphere to not roll and just slide?
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1answer
57 views

When and why are we allowed to treat a rigid body as a point mass?

When the subject Mechanics first taught, it is common that we explicitly state that the Newton's laws are valid only for point masses, and then we give examples of rigid bodies colliding with each ...
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0answers
179 views

Start of gyroscopic precession

Let's consider the classical example, the wheel hung by one side of the axle: ¹ When the wheel is not spinning, it will tilt down the free end of the axle first. When the wheel is spinning, it will ...
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0answers
146 views

Proof of holonomic constraints for a wheel on a track

I'm faceing a problem of a thin wheel of radius R rolling without slipping on a track (y = f(x); on xy-plan). The wheel plane stays vertical and tangent to the track at the contact point P. $\alpha$ ...
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1answer
245 views

Gyroscopic precession - Angular momentum in vertical direction

In the classic example of gyroscopic precession, the wheel starts to process, and now acquires a angular moment also in the vertical direction. Initial angular momentum was in a single plane. The one ...
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2answers
178 views

Is kinematics required to solve for the quaternion dynamics of a tumbling body?

I'm trying to solve for the rotational motion of a rigid body in the absence of external torques using quaternions in MATLAB. Assuming the axis of rotation as the unit vector $\begin{bmatrix}a_x & ...
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0answers
45 views

Matrix Euler’s rigid-body equation

Define the action $$S[g]=\displaystyle\frac{1}{2}\int^1_0 Tr(I(g^{-1}\dot g)~g^{-1}\dot g)~dt.$$ $I:SO(N)\to SO(N)$ denotes the endomorphism $\omega \to I(\omega)$ with $I(\omega)_{ij}=\omega_{ij}/...
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1answer
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Uniqueness of Mass Moment of Inertia tensor

I was curious to know if there can exist two different objects (shape and/or mass distribution) that can have the same inertia tensor.
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2answers
311 views

The angular velocity

Is the angular velocity of a rigid body about any point the same as that about the axis of rotation. Also, can we even define angular terms (Angular Velocity, Angular Acceleration, etc) about any axis,...
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1answer
840 views

Relation between acrobat and principle of conservation of angular momentum

How the principle of conservation of angular momentum is used by an acrobat to rotate a few revolution while leaping throung the air?
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39 views

Velocity of the reverse/double domino effect

I've seen a lot of talking about the propagation velocity of the domino effect, and I've even read a very interesting paper called 'The Domino Effect' by Leeuwen which really satisfied me. And yet, I'...