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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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 ...
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4answers
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Angular momentum and torque in gyroscope

In my textbook (Kleppner), the principle of a gyrocompass is given to be "A flywheel free to rotate about two perpendicular axes tends to orient its spin axis parallel to the axis of rotation of the ...
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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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Euler's Equation of Motion by Lagrange's Equations [duplicate]

currently i am studying three dimensional rigid body dynamics. My question is how to derrive the popular Euler's Equation of motion given by: $\sum M_x = J_x\dot{w}_x-(J_z-J_y)\omega_y \omega_z $ $\...
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1answer
76 views

Rotational motion integration (Rigid body dynamics)

I am trying to integrate the rotational motion of a rigid body (a set of N point masses) $\textbf{in the inertial frame}$, but my results seem totally wrong. What of the following steps could be wrong?...
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Does direction of angular velocity/acceleration have any physical implications?

when first learning about the angular velocity/acceleration, the right hand rule is mentioned. According to it, the direction of angular velocity/acceleration is along the axis perpendicular to the ...
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1answer
34 views

What's the name for “middle” principal axis of inertia?

See this question for some context about the stability of rotation of a body around different axes. I am now trying to say that the rotation around the middle axis is very unstable, without using ...
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Frame-referenced time derivatives

I have reviewed and am familiar with the similar questions asked and answered previously on this forum, the various Wikipedia references and the derivation used by Kane and Levinson [2]. The ...
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29 views

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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1answer
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What makes a forever spin top special?

What is the difference between a regular spin top and a forever spin top (which spins for far longer than a regular spin top).? The forever spin top is made out of stainless steel. I would like an ...
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2answers
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In the derivation of centre of mass, what is the basis of assumption a point having same acceleration as the body?

In the derivation of centre of mass, we assume that a point $X$ exists such that its acceleration is the same as acceleration of the whole body. And as the derivation proceeds, this point comes out to ...
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3answers
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What justifies the use of centre of mass?

Centre of mass gives the location where the 'weighted average' of all the elemental mass of a body acts. Considering that weighted average is one of the many statistical tools used to find the spread ...
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Nutation angle calculation of spacecraft

I need to calculate the nutation angle of a spacecraft for different timesteps. I have a file which gives me the angular velocity $~w = (w_x,w_y,w_z)~$. When no torque is applied, the inital angular ...
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Nutation Angle calculation out of attitude Data

I have a rocket body with given Euler Angles, Quaternions and Angular-Velocities for given time steps. And I'd like to calculate the Nutation-Angle for every time step, so that I can plot the cange of ...
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Man standing on railroad car and rotating with it

The above picture shows a man of mass M standing on a railroad car which is rounding an unbanked turn with speed v. The man is facing the direction of his motion. The centre of mass of man is height L ...
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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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3answers
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Finding Direction of Angular Velocity

Suppose I have a 3D rigid object on which some external forces act at various points located on it. The resulting motion would, in general, be the translation of center of mass plus rotation about the ...
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Rigid body dynamics exercise

Yesterday I came across this exercise and I can't really find a way to get the correct answer. Exercise A rigid homogeneous rod that weighs $M=5\,\mathrm{Kg}$, has length $l=0.8\,\mathrm{m}$ and a ...
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2answers
59 views

Centre of mass of a solid cone using a symmetrical method [duplicate]

When we rotate a right angled triangle about its perpendicular we get a solid cone. For a right-angled triangle the centre of mass is at its centroid i.e., at $(\frac h3, \frac b3)$. If we consider a ...
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1answer
21 views

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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2answers
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How to figure out the distribution of Normal Force on a body?

I was solving a problem and came across some confusion regarding the point of application of Normal Force. In Classical Mechanics 101, we had always treated the Normal Force as acting on a point (...
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0answers
44 views

How does friction cause a spinning top to fall?

I am wondering how friction can create a torque to change the angular momentum and cause a spinning top to tilt, like in the diagram of a close up of the rounded tip of a top while the angular ...
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What are the limits of spin speed on a graphene ribbon?

In my previous question, link below, I asked what are the limitations on spinning an object with the goal of achieving relativistic speeds at the edge of the spinning object. In the comments, someone ...
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1answer
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Rigid body dynamics: modelling a polygon bounce off ground

I'm currently making a physics simulator, but I'm having some trouble making a polygon bounce off the floor. I know that collisions are normally modeled as described below by ja72, but I did it ...
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1answer
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Does an asymmetric top return to its initial position &orientation, while rotating freely in space? (contradiction in Landau&Lifshitz mechanics book)

The Poinsot's ellipsoid tells us that the angular momentum ($M$) (in the rotating frame) should be lying on the intersection curve between the conservation of momentum sphere radius $|M|$: $M_1^2 + ...
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3answers
146 views

Is flipping a coin is a stable rotation?

If I rotate a coin with dimensions: 10X10X1 about 1 of the big axes(10) in space, where there is no torque, will the rotation will be stable just like a frisbee or a football regular rotations are? ...
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1answer
106 views

Balance of a rolling coin

If we place a typical coin on a table, it will almost immediately fall due to gravity. However, with a little push it will roll and not fall anymore until friction eventually slows it down enough to ...
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0answers
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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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1answer
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Rigidity or Bodies with Triangular Shapes of Faces

Originally I read an answer on Quora wherein the author showed that by using magnets he made different shapes. Squares were easily deformed, so we're other shapes with square faces such as cubes ...
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1answer
48 views

Does asymmetric rigid body experience torque-free precession?

I know that a top (or any axis symmetric body) experience torque-free precession. and I know that asymmetric body, with 3 different dimensions has stable rotation when the angular velocity is near the ...
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0answers
26 views

Finding the total rotation about an arbitrary axis

I have a rigid body which is fixed in a x,y,z system and is free to rotate. The z vector is parallel to gravity. x and y are arbitrary and perpendicular to z. The moving coordinate system is x',y',z' ...
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1answer
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Why conserve angular momentum about COM

In many questions involving collisions between Rigid bodies angular momentum is conserved about center of mass If bodies stick together after collision they estimate com and then conserve about ...
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2answers
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What are the possible method to simulate the dynamics of rigid bodies in simulation? [closed]

I just want to know the name of the methods, the simulation physicist uses to simulate the dynamics of rigid bodies. Eg. Impulse Based Dynamics developed by Mirtich
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1answer
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Rotation of a rigid body within another orbiting body [closed]

I would like to understand the physical behaviour of the following rotating sytstem. There are 3 rigid bodies (1 is blue, 2 are red). We assume that there is no friction between the blu body and the ...
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0answers
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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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3answers
65 views

Z-shaped lever balance

The goal is to find out whether a Z-shaped lever will fall over due to gravity. See diagram below (sorry for MS Paint): The bottom edge $x$ is resting on a flat surface. All three edges, $x$, $y$, ...
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0answers
22 views

Degrees of freedom [duplicate]

Consider a system of 10 (say) point particles each at a fixed distance from each other in 3-D space. In this case, the number of degrees of freedom: $3*(number-of-particle)-\binom{10}{2}=3*10-45<0$ ...
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5answers
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Rolling object not stopping even when friction is considered

I am dealing with a question that has me puzzled. Suppose an object which is rolling on a horizontal plane, with initial linear velocity $v=v_0$ and angular velocity $\Omega=\Omega_0$. There is ...
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0answers
23 views

Derivation of Equation of motion from Euler-Lagrange Equation [duplicate]

Hello I am new to Lagrange's dynamics and have some doubts regarding derivation of equation of motion given in a text : Deriving Equation of motion for a free body(no-external forces) ,in one ...
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1answer
76 views

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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1answer
57 views

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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65 views

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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0answers
290 views

Newton's second law in angular form [duplicate]

I'm rather confused about the correct form of Newton's second law in angular form and how matrices of inertia could be converted from one coordinate system to the other. Consider the system below: ...
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2answers
133 views

Angular velocity of rotating rod

Consider the following system: Newton's second law for rotational motion: \begin{equation}\tau=I\alpha \Leftrightarrow rF=\frac{1}{3}mr^{2}\alpha \Leftrightarrow \frac{d\omega}{dt}=\frac{3F}{mr}\end{...
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0answers
26 views

Is it possible to find the linear and angular forces?

Suppose an object has both linear an angular motion. Let's consider the object a sphere. What we know: - The angular velocity and acceleration - The linear acceleration of the center of mass. - The ...
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0answers
29 views

Euler Lagrange 2D equation of motion of flying object with inverted $z$-axis

I have the following 2d problem. A flying object of mass M carrying a rigid cable of length L with an attached mass (m) at the end, is described by the following scheme: With $\alpha$ the angle ...
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31 views

Conservation of Angular Momentum about the Instantaneous centre of rotation

While solving some problems on rotational kinematics involving ,say, a cylinder rolling without slipping against a rough surface, I used conservation of angular momentum about the instantaneous centre ...
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0answers
35 views

Factors effecting the time period of Euler's disk [closed]

I wish to carry out research on the factors effecting the time period of a spinning Euler's disk. Do factors like friction coefficient of the base or concavity of the base effect the disk? If not, ...
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1answer
26 views

Parallel axis theorem of stick-ball configuration

I have a system with a rod of mass m and length 2a. Let the origin be in the middle of the rod at x = 0. (Therefore, each end is a distance a away.) A ball of mass m is attached to the far right end. ...
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52 views

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, ...