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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How can precession produce a torque in the direction of precession when it has no angular momentum?
I this video, an 8 lb gyro on a rod supported at one end is spun up to several thousand rpm, and an assist is use to get the axis nearly horizontal. A small stick is used to nearly instantly stop the ...
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Quadcopter motor speed mixing
I'm having trouble solving the following problem. I've designed a control system for a quadcopter, my design is built upon a nonlinear model in the affine form:
$$
\dot{x}=f(x)+g(x)u
$$
The system ...
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63
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Distribution of contact forces on a square at rest
Consider a square (blue) on top of a platform (yellow), on which gravitational force (black) acts. We know that if the blue square is in equilibrium, contact forces from the platform (white) must act ...
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Moment of Inertia of a Rectangular Parallelepiped
Moment of inertia calculated about an edge for a rectangular parallelepiped is given by
$$I = (m/3) (a^2 + b^2), $$
my question is:
when m(a^2+b^2) is added to I, the new value obtained is Moment of ...
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Is it possible to model the rotation of a bowl as a function of time?
I was watching a video where someone spun a bowl, and then let it rotate until it eventually stopped and fell flat onto the table. I was wondering if it is possible to model the rotation of a bowl as ...
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Kinetic energy of rigid bodies about the center of mass
Suppose, we have some rigid body, that is rotating about some pivot. In this case, we can easily find the kinetic energy, by choosing a random point $P$ on the body. The kinetic energy of the body ( ...
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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 ...
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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 ...
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How to model friction in physics engines
How does one model and simulate friction in Rigid body systems?
For example a rigid box moving across a plain which has variable friction coefficients with respect to location. It's not clear to me ...
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Instantaneous axis of rotation for a cylinder
In Landau's Mechanics volume at section 32 solved problem no. 5, the instantaneous axis is chosen as the one which coincides with the line where the cylinder touches the plane. This is possible only ...
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Angular velocity of a cylinder rolling in another cylinder
I'm having troubles with the following problem:
Consider a hollow cylinder of radius $2R$ which has a point of its rim fixed in an inertial frame and can rotate about this fixed point. Inside it there'...
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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 ...
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How can I prove the existence of rest points in rigid motion with all speeds orthogonal to $\vec{\omega}$?
If in a rigid motion there is a point at rest, then all speeds are normal to $\vec{\omega}$ (assumed $ \neq \vec{0}$), to prove choose the rest point as origin and explot fundamental equation of rigid ...
user291161
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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 ...
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Rigid Body Dynamics - How do objects move in loops?
I have been attempting to simulate the motion of a (heavily) simplified model of a rocket using MATLAB's Simulink, but I am not seeing behavior that I expect (intuitively, and I am very open to being ...
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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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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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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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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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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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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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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 ...
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Mathematical Derivation of the Condition of Equilibrium of a Rigid Body
We know that for a body to be in equilibrium, the resultant force and resultant torque must be both zero. The question is: can we derive this from more fundamental principles mathematically, such as ...
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Confusion about relation between inertial an non-inertial reference frames in respect tto the motion of a rigid body
In "Analytical Mechanics" by N. A. Lemos, in page 99 the author determines the time derivative relation between an inertial frame $\Sigma$ an an non-inertial frame $\Sigma'$ fixed in a ...
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101
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How exactly does a control moment gyroscope work?
I've searched a lot, but have not been able to find a proper explanation for the working of a control moment gyroscope. Could someone please explain it to me, preferably with vectors?
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Acceleration of a merry-go-around, when a human is walking along it's rim
According to law of conservation of angular momentum, the merry-go-around is expected to rotate at constant angular velocity, while the man walks along it's rim with constant speed relatively to the ...
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Generalized coordinates of two unequal masses attached to a mass-less rigid rod
Consider a system of two particles of masses $m_1$ and $m_2$ moving in a plane. Let the respective position vectors be $\mathbf{r_1}$ and $\mathbf{r_2}$. The particles are attached at the end of a ...
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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.
...
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Changing axis of rotation?
Let's say I've got a massless rod, at the end of which, I've attached 2 identical balls. Now say I drop the rod, such that it collides with the ground and for some reason, the coefficient of ...
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Simulating Rotor Blades for Quadcopter
I would like to simulate various shapes for rotor blades that will be used in a quadcopter. Which simulation software is used to understand how shapes, rotation interacts with the surrounding air? I ...
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3
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650
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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 ...
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What is the interplay between the "spinning tennis racket" effect on a planet with three principle axis of rotation and its moon?
Suppose I have a tennis racket spinning on its second axis of rotation such that it is subject to periodically flipping over on its spinning axis, as per the Dzhanibekov effect (explained in ...
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A query on the solution of a gyroscope with friction
I have been trying to solve the motion of a gyroscope with friction added, so that as in reality, its spin will slow down with time. My first naive attempt to add friction has run into trouble and I ...
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Measurements taken in Euler's equation of rigid body motion
I am having some confusion about the frames involved in Euler's equation of rotational motion.
$$
\mathbf{I} \dot{\boldsymbol\omega} + \boldsymbol\omega \times \left( \mathbf{I} \boldsymbol\omega \...
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Kinetic energy of a solid
Considering an inertial reference frame with origin O, the first part expresses the angular momentum of a system as the sum of the angular momentum of the center of mass and the angular momentum ...
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Does the mass of a rigid-body affect its bounce?
I'm working on a computer program which involves some physics. I want to know if the mass of a perfectly rigid ball will affect how high it bounces off the ground. I'm in high school and I haven't ...
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How to calculate/use horizontal coefficient of restitution value for basketball?
I'm trying to run an experiment in which a basketball is dropped straight down with a certain angular speed and then undergoes a bounce. My goal is to create a relationship between the initial angular ...
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How to calculate the tensor of inertia in this problem?
I have the following geometry for my problem:
I'm asked to calculate the tensor of Inertia:
$\stackrel{\leftrightarrow}{I}_{O}=\left[\begin{array}{ccc}{I_{11}} & {-P_{12}} & {-P_{13}} \\ {-...
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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 ...
- 1,183
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Derivation of the time-derivative in a rotating frame of refrence
I have so trouble following Goldsteins derivation of the time derivative in the rotating refrence frame, and its use to derive the coriolis force (sec. 4.9-10) Given an intertial frame of refrence, $S$...
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Does rigid body rotation always add a new independent variable?
I want to talk about the constrain added by introducing rotation of a rigid body to a simple case:
An homogeneous ring at rest is dropped from height $H$ of an declined surface without any kind of ...
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If there was no friction would a thin rectangle with mass $m$ with sides $a$ and $b$ spin indefinitely about an axis through its diagonal?
I would like a geometrical physics answers so I can have an intuitive grasp about the problem. That means no nonphysical things like matrices, coordinates and random basis of vectors.
For example it ...
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How a stick in space moves when force only acts on one end? (suppose stick is rigid body)
I am confused with how to put inertia in to this problem, which suggests the end the force acts on should move first while another end remains fixed at first moment.
I think that the stick should ...
- 1
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Effect of spin on the deflection of a rigid body
Suppose an x-y coordinate axes is set on the ground, then a spherical object is projected in the forward direction (the positive y direction) and while moving in this forward direction it also ...
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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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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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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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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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Approximation of motion about instantaneous center
I am trying to do kinematic analysis of suspension.My doubt is that can i find Trajectory of my Suspension joints by rotating these points about the instantaneous center and again finding the new ...
