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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Lagrangian preserve it's form for rigid bodies
Lagrangian for a particle moving under influence of conservative force given by
$$\mathcal{L}=T-V$$
that is Kinetic energy minus Potential energy. Now for a system of particles I expect the same form ...
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Tension on a massless string holding a semisphere in place
I am having trouble solving this. The problem is the following:
Suppose a semisphere of radius $a$ (with its center of mass at $h = \frac{3}{8}a$) of mass $m$ located on a sliding surface. A massless,...
user146820
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The torque in Euler's equations for rigid body rotations
In Taylor's Classical Mechanics, it is said that the equations are generally difficult to use because the components $M_1,M_2$ and $M_3$ of the applied torque as seen in the rotating body frame are ...
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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 ...
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Does gimbal for education exist?
I have been looking for a gimbal for a long time. Something similar to what you see in the book.
However, I have had a lot of problem to find something similar. All my search results end to
%95: ...
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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. ...
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The Ehrenfest paradox and materials science
There are many questions on the Ehrenfest paradox but I couldn't find a duplicate (which may stil exist).
The rim of a rotating disc would be Lorentz-contracted as seen from a non-rotated observer ...
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Equivalent fictitious forces on rigid body
I know that when I study the motion of a rigid body from a non-inertial frame, I have to take into account the fictitious forces.
However, it is not straightforward to find the resultant force (and ...
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Is there a fixed orientation of center of mass axis about which all unconstrained rigid bodies rotate?
I just learned that an unconstrained rigid body always rotates about its center of mass. But there could be many axes that could pass through the center of mass.
For example, let's consider a rod ...
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How many illusionary axes of rotation can coexist?
Consider the answer to this question:
How many different axes of rotation can coexist?
Any rigid body, at any time, can only be rotating about one instantaneous axis of rotation.
Now, that ...
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Accion response calculation on tilt steering kick board scooter
Hi I am designing a home made kick board scooter, need to understant
the behaviour between the board angle and the turn angle.
In a classic sakateboard the foot action is transformed to turn angle,
...
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Nutation frequency for a weighted gyroscope
So, I've been led to believe that the frequency of nutation of a gyroscope can be calculated using the formula
In which the I's are the moments of inertia around the principal axes and omega-3 is the ...
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Ideal geometry for a shaft terminating thrust bearing
Following this PyDy example, I'm trying to understand the problem set 3.10 of the book:
Kane, Thomas R., and David A. Levinson. Dynamics, theory and applications. McGraw Hill, 1985.
page 272 (292 ...
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Insufficiency of Newton's third law to solve constrained motion problems
In The Variational Principles of Mechanics Lanczos describes what he calls 'vectorial mechanics': the process of solving mechanical problems by recourse to the immediate consequences of Newton's laws, ...
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How to calculate the viscous damping coefficient of a viscous layer between an inner sphere and an enclosing outer sphere?
In this article by Rahn and Barba, a flat-spin transition manoeuvre is investigated. For this it is assumed that a rigid spacecraft contains a spherical, dissipative fuel slug of inertia $\boldsymbol{...
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What is centre of rotation and a ref. point fixed wrt to the body?
I'm studying Analytical Mechanics, and in the section about the kinematics of rigid body, it is mentioned the following concepts:
Center of rotation
a reference position that is fixed with ...
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Angular Momentum and assymetric axis
The question I came across ,
If a semicircular disc rotates uniformly (const. angular velocity) about an axis passing through its Centre of mass , and prependicular to its plane , do we need an ...
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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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How can non-body-fixed angular velocities can be approximated by co-moving ones?
When reading a paper about magnetic bearings, I have stumbled upon the following ansatz which I don't fully grasp (page 3):
For a general body, the Euler equations are given in a body fixed
...
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Two dimensional ball motion on a plane
Suppose i have a horizontal table. Choose a standard cartesian coordinate such that the $x-y$ plane coincise with the table. Assume that the table is not smooth. Suppose i have a solid ball with ...
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Measurement location on a rigid body
I am just wondering if it is possible to calculate/estimate the location of measurement point on a rigid body?
For example, lets say we have a rigid body that is in motion. We attach a sensor, say an ...
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Orthogonal matrix of operators (and the quantum rigid rotor)
While reading the section on the rigid rotor in Weinberg's Lectures on Quantum Mechanics I have found a problem when dealing with a matrix of operators. First of all, clasically, to describe a rigid ...
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Forces (Using Lagrange multipliers) of a fixed bicycle wheel
I'm having doubts about my Lagrangian when I release my constraints:
I'm using Euler angles and using a system which is referenced to the wheel. It's quite straightforward to get the Lagrange ...
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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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Angular Momentum
I have several questions about angular momentum.
I know there are 2 parts of angular momentum - translational and rotational. For a body with respect to a fixed point, translational angular momentum ...
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'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.
$$m\frac{dw_G(...
user24370
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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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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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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 ?
why ...
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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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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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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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Question about Euler's equation for rigid bodies
I wished to understand a particular case of Euler's equation applied in the following cylindrical body:
where $I_{1,2,3}$ are the moments of inertia. By symmetry, $I_1=I_2=I_T$.
Here I consider that ...
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Off center, perpendicular force applied to rigid body with pivot/ fulcrum at center of mass?
I feel like this question has been asked in so many ways, but I am still unable to explain my personal experience based on previous answers. From other discussions:
You can always replace an off-...
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Angular Velocity in the Plane of a Lamina
A rigid body (i.e., a 2-dimensional object) has principal moments of inertia about the centre of mass of $I_1 = (\mu^2 -1), I_2 = \mu^2 + 1, I_3 = 2\mu^2.$ I wish to show, using the Euler equations, ...
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Derivation of the Lagrange equations of motion from d'Alembert's Principle specifically for rigid bodies
All of the proofs of the Lagrange equations of motion from d'Alembert's Principle I've seen so far deal exclusively with the force-inertial force balance for particles ($F-ma=0$). Despite this, the ...
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Calculation of Accelerometer offset for Placement of Inertial measurement unit away from centre of mass
I am working on a 6DOF IMU that contains a 3-axis accelerometer and a 3-axis gyroscope, I am building a project to
plot the position and orientation of a vehicle/dirt bike in a 3d plane, However the ...
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Self-Balancing Electric Unicycle - rider lean required for acceleration | deceleration - torque effects
A self-balancing electric unicycle consists of a frame+pedals that the rider stands on, a motor where the stator is attached to the frame+pedals, and a rotor which is attached to the wheel+tire.
An ...
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How does the inertia tensor change when a rigid body is mirrored/flipped?
Suppose I have a rigid body $A$ whose center-of-mass is located at $\vec{u}=(u_x,u_y,u_z)$. Furthermore, let its principal axes of inertia be $\{\vec{a},\vec{b},\vec{c}\}$ and $I$ be its inertia ...
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How to update the state of a rigid body after an impulse is applied?
When evolving rigid bodies using forces you integrate the force applied along the COM and integrating the torque using eulers equations of motion.
I am confused on how you approach this problem using ...
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Can the angular velocity of a prolate spheroid change over time in the absence of external forces?
Given a prolate spheroid (ie a Rugby Ball/American Football), with an initial angular velocity about an axis that coincides with one of the shape's primary axes, it seems obvious that in the absence ...
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Infinitesimal work done by a single force on a rigid body
Let there be a rod lying on a frictionless surface (or just in deep space). A constant force $\vec F$ acts on the rod for infinitesimal time internal. The force acts at a point located at some ...
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Transformation of coordinates
I asked a couple variations of this question before but neither really answered my core question(which I maybe did not present).
Suppose we have two coordinate systems, $F_1$ and $F_2$ fixed together ...
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Uniform rod tipping over the floor
That's an exercise from Thorton's Classical Dynamics textbook.
Basically, as stated, a uniform rod of lenght $b$ tips over to the floor, being initially stood vertically upright on the same floor. The ...
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Can a thin hoop rolling without slipping on a flat surface experience friction?
Take a smooth rigid body (cylinder,hoop,sphere,etc.) rolling on a flat surface. Then, supposing the body experiences a friction force $f$ at the contact point,
\begin{equation*}
ma = f
\end{...
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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 ...
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Spring forces with constraints
I am not making progress with understanding with all forces acting on a falling object that collides with an unmovable floor. I want to simulate a car shock absorber attached to a weight falling and ...
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How to compute the eigenvalues and eigenvectors of the pseudo inertia matrix?
The pseudo-inertia matrix is defined as
$\widetilde{\Xi}=\left(\begin{array}{cccc}\frac{1}{2}\left(-I_{x x}+I_{y y}+I_{z z}\right) & -I_{x y} & -I_{x z} & m c_{x} \\ -I_{x y} & \frac{1}...
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Moment of Inertia of Higher Dimensional Objects
I would like to take on the mathematical exercise of deriving expressions for the moment of inertia of higher dimensional solids. But could there be any real world utility to it? If yes, which fields ...
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