# 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 I approximate Jacobian Elliptic Functions in terms of basic integrable functions for the $\operatorname{SO}(3)$ rotation of a rigid body?

So, the rotation of a 3d body can be described with Euler's equations of motion giving the rotational velocity in components along the principal axes of inertia. As shown in f.ex. this paper, Euler ...
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### Goldstein Classical Mechanics exercise 5.17 (3ed) conceptual

I am having difficulty understanding a concept in the "Heavy symmetric top" type of problems. I will include all of my efforts as to hopefully have someone easily point out what it is that I'm missing....
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### How to apply a screw motion for this case?

I'm completely new to the notion of a screw motion. As far as I know, it carries out the the rotation and translation simultaneously in comparison with the homogenous transformation matrix that ...
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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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### 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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### Is there an egg that rolls infinitely far with no starting momentum?

This occurred to me when making an omelet. I want to construct a 3-dimensional rigid egg that when placed stationary on a flat surface with no friction or slipping either rolls to an unbounded ...
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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? $$(d\textbf{G})_{space} = (d\textbf{G}... • 148 3 votes 0 answers 600 views ### Start of gyroscopic precession Let's consider the classical example, the wheel hung by one side of the axle: ¹ When the wheel is not spinning, it will tilt down the free end of the axle first. When the wheel is spinning, it will ... • 1,580 3 votes 1 answer 127 views ### These components of the angular velocity are given in what reference frame? When we have a rigid body, the rigidity constraint allows us to write the trajectory \mathbf{r}_i of the i-th particle as$$\mathbf{r}_i(t) = R(t)\mathbf{b}_i + \mathbf{w}(t),where we are ... • 33.8k 3 votes 0 answers 710 views ### Torque due to air resistance on a frisbee In my analytical mechanics course we worked out an example involving a disk (say, a frisbee) rotating after being thrown into the air. The disk experiences a torque proportional to its angular ... 3 votes 0 answers 108 views ### Is there a form of rigid body dynamics that uses unit quaternions instead of Euler angles? I’d like to know specifically about an elegant way of deriving a second derivative of an orientation quaternion from a torque and a moment of inertia matrix, if one is available. The straight forward,... 3 votes 0 answers 185 views ### Analysis of motion of a body moving on a string? I was wondering about something I observed yesterday. To give some background, one of my hobbies is slacklining. This is essentially like tight-rope walking but with a one inch piece of (in this case ... 3 votes 4 answers 474 views ### Degrees of Freedom for an Asymmetric top How many degrees of freedom does an asymmetric top have if it is rotating about a fixed point?What are the generalised coordinates used then? • 31 3 votes 0 answers 125 views ### Gauge formalism in rigid body mechanics When doing calculations in rigid body mechanics, it is necessary to choose an origin to calculate torques and angular momenta. However, the underlying dynamics does not depend upon the choice of that ... 2 votes 1 answer 57 views ### Quantum Mechanics of a rigid body that has only finitely many possible axes of rotation I consider the quantum version of dynamics of rigid body motion with intrinsic angular momentum, having moment of inertia I. Given a classical free system of one free rotating spherical rigid body (... • 472 2 votes 1 answer 43 views ### Two questions regarding Spivak's Configuration Space The following is from the fifth Chapter Rigid Bodies of Spivak's Physics for Mathematicians. The post consists of a statement Spivak makes -with no proof- that I do not understand. For clarity, I've ... • 363 2 votes 0 answers 72 views ### How does Schwarzschild spacetime bend a free falling rigid body? How does Schwarzschild space-time bend a free falling rigid body? Will it be stretched or squeezed? How much it will be modified? Can we find an effect of Lorentz contraction? When will the assumption ... 2 votes 0 answers 55 views ### Inertia tensor for rotors For vectors we can use Inertia tensor. But if I want to use bivectors (Rotors), what should I use for the inertia tensor? I want to make a 2d game and progressively to 4d. • 23 2 votes 0 answers 83 views ### Dynamics of interconnected rigid bodies using Newtonian physics Passive SONAR uses a towed array system to hear the underwater sound uninterrupted. This towed array sonar is a system of hydrophones towed behind a submarine or a surface ship on a cable. The ... 2 votes 0 answers 159 views ### Proving that the relative angular velocity of any particle with respect to any other particle is the same in a rigid body Claim: The angular velocity of any point mass of a rigid body relative to any other point mass is the same, i.e., \vec{\omega_{i,j}} = \vec{\omega}\;\,\forall{i}\,\forall{j}, where \vec{\omega} is ... 2 votes 1 answer 144 views ### Non-Holonomic constraint in rigid body dynamics I have solved many problems on Holonomic constraint using Lagrange multiplier method but I don't know how to tackle problems on non-Holonomic constraint. Can anyone help me with the following problem ... 2 votes 0 answers 166 views ### 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 ... • 21 2 votes 1 answer 341 views ### Confusion regarding torque and calculating linear/angular acceleration of an object when a force is applied a distance from its center of mass? From what I have read/learned about torque, it appears that it is derived based on the idea that applying a force farther from a point about which an object rotates increases the rotational force ... 2 votes 0 answers 103 views ### Physical interpretation of the definition of angular momentum in classical mechanics To what I understand, the following is a valid way to introduce the angular momentum \mathbf L in the Lagrangian system of a rigid body. We can consider the extended configuration space to be M\... 2 votes 0 answers 498 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 ... • 49 2 votes 0 answers 107 views ### Wheel rolling leaned against a vertical wall I'm new with rigid problems about. I'm trying to solve this: A massive circular disk of mass m, radius R, and negligible thickness is leaned against a vertical wall, slanting by 45 . In the ... 2 votes 0 answers 96 views ### Terrestrial Space Elevator Construction - Plausability Framework If there was a cable constructed at the equator about the circumference of the Earth, and if this cable had sufficient strength to remain intact while erect, call this tensile strength T. ... 2 votes 0 answers 219 views ### Movement of a gyroscope with non-fixed axis Assume one has a gyroscope rotating around an axis with both ends leaning on a dedicated semiplane as shown on the picture below. There is no friction either between the rotor and the axis or between ... • 121 2 votes 0 answers 207 views ### What kind of shape has the lowest flutter wind speed? What kind of shape has the lowest flutter wind speed and is the most unstable? I mean for rigid body. Thanks Yes, I know many factors affect the flutter in a MSD system (for rigid body), however I'... • 613 1 vote 0 answers 33 views ### Is Energy conserved in a spinning top? When we spin a top (give it kinetic energy K_0) and place it on a table, it starts precessing around the vertical axis. Is the total energy of the spinning and precessing top equal to the initial ... • 1,108 1 vote 1 answer 27 views ### What does it mean to take a mass moment of inertia about a single point? This website here: https://www.chegg.com/learn/calculus/calculus/moment-of-inertia-about-the-origin Shows the following: How is it possible to define a mass moment of inertia about the origin which ... 1 vote 0 answers 33 views ### Proof of principle of transmissibility of force The principle of transmissibility states The point of application of a force to a rigid body can be moved anywhere along its line of action without changing the external reaction forces. My question ... 1 vote 0 answers 27 views ### Acceleration of Centre of Mass immediately after the application of Force I read it in my physics textbook about the application of Force on Rigid Bodies and there I came across this case:- So now here when force is applied to this rod which is fixed at an end [represented ... 1 vote 0 answers 26 views ### About the coincidence of angular momentum and angular velocity Let me quote part of the answer by @knzhou , posted here "In very basic introductory physics courses, you will usually only consider rigid bodies with an axis of symmetry, rotating about that ... • 10.4k 1 vote 1 answer 128 views ### Why don't Euler's formulas for torque apply to this problem? In my mechanics class we were assigned problem 9.44 from "Introduction to Classical Mechanics" by David Morin as homework. The problem and figure are below: Two wheels of mass m and ... 1 vote 2 answers 64 views ### Why is studying individual particles in a rigid body not correct? And questions about momentum I've just come across an exercise that consists of a rigid, ideal rod that can move around a fixed axis: After letting it move , the rod's angular velocity at time t (when it is vertical) is asked. ... 1 vote 1 answer 63 views ### Moment of inertia of irregular object How could you use a torsional pendulum to determine the rotational inertia of any object that could be mounted on the Rotary Motion Sensor?` Note: The Vernier Rotary Motion Sensor is a bidirectional ... 1 vote 0 answers 34 views ### Quasi-rigid bodies in relativity and decomposition of energy In relativity there can be no perfect rigid solids, the Born rigidity is as close as you can get and yet it is severely constrained (Herglotz-Noether theorem). For that reason, rigid solid mechanics ... • 1,237 1 vote 1 answer 124 views ### Are the velocities of a falling rolling coin/wheel parallel? Can someone confirm that a rolling coin that is falling will, at any instant, only have horizontal velocity directions that are parallel (those velocities being horizontal component velocities)? It is ... • 71 1 vote 0 answers 56 views ### How to calculate degrees of freedom? Background I am trying to run optimizations on a multilink (car-) suspension. That is each link is defined by two points, one on the vehicles body, one on the wheel mount. There are 5 links in total, ... • 111 1 vote 1 answer 93 views ### Why is the sum of torques for each particle equal to the external torque? Let's assume we have a rigid body. The internal forces all have equal and opposite counterparts so the they will produce a net zero torque. We can therefore ignore internal forces when calculating the ... • 303 1 vote 0 answers 32 views ### How can the total torque of a body equal a "torque" at only one point? I am trying to understand the solution to this problem. Pictured is a rough sketch of a ball in which another, smaller ball of density \rho_2 > \rho_1, where \rho_1 is the density of the ... • 11 1 vote 0 answers 53 views ### Derivation of rotational body interia from newton's laws We know that rigid body will keep rotating without external force. This answer explains Rotational inertia differs from ordinary “linear” inertia in that it is a derived principle: it can be derived ... • 123 1 vote 1 answer 19 views ### Does the height a person jumps from onto a rod, affect the rotational height of a rod? I was explained in a lecture that if lets say, I jumped from height h and grabbed onto a vine, I would reach y height at the tip of the swing. But if I were to jump from 2h, I would still reach the ... 1 vote 0 answers 67 views ### Modeling Golf Ball rolling around in golf hole I am trying to model a rotating/rolling golf ball’s interaction with a golf hole. The boring case is just the ball rebounding in an elastic collision off the wall, with conservation of momentum ... • 111 1 vote 0 answers 132 views ### Q: Landau Vol. 3, Section 103 (3rd ed.) Quantization of the rotation of a top Have been reading section 103 of L&L quantum mechanics, and have some problems with understanding/interpretation. Hope someone can help out. In the section it is said that the coordinate system \... 1 vote 1 answer 137 views ### 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)\... • 11 1 vote 1 answer 66 views ### 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 ... • 121 1 vote 0 answers 125 views ### 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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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 ...