Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

2
votes
5answers
66 views

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 ...
0
votes
0answers
21 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 ...
1
vote
1answer
34 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 ...
0
votes
0answers
47 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 ...
0
votes
0answers
35 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 ...
0
votes
0answers
286 views

Newton's second law in angular form

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: ...
1
vote
2answers
39 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{...
0
votes
0answers
21 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 ...
0
votes
0answers
23 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 ...
1
vote
0answers
27 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 ...
1
vote
0answers
33 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, ...
0
votes
1answer
22 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. ...
0
votes
0answers
43 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, ...
0
votes
0answers
20 views

Rigid body in a vector field

If I let a particle with coordinates $x(t)$ move in a vector field $F$ the equation I have to solve is $x'(t) = F(x(t))$, right? But if, instead of a particle, I have a rigid body, which equation I ...
0
votes
1answer
24 views

Does moment of inertia only work for special cases?

I was looking into the moment of inertia expression for angular momentum. The angular momentum of a group of particles can be expressed as a linear transformation of the angular velocity vector. This ...
0
votes
0answers
23 views

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
vote
1answer
77 views

Rotation matrix - levi-civita symbol

I'm trying to solve the following problem: Given a rotation matrix $R_{ij}$, show that $$n_k=\frac{-R_{ij}\epsilon_{ijk}}{\sqrt{(3-tr(R))(1+tr(R))}}$$ and that $$\sin(\phi)=-\frac{\epsilon_{ijk}...
0
votes
1answer
47 views

Kinetic energy of a yoyo

Consider the yoyo above: The yoyo is constructed from two heavy disks of radius R connected by a light axle of radius r , as shown in the figure below. The total mass of the yoyo is M and its moment ...
1
vote
0answers
100 views

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{...
1
vote
0answers
17 views

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 ...
0
votes
1answer
22 views

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 ...
1
vote
2answers
69 views

Rigid body dynamics derivation from Newton's laws for higher dimensions

Since Newton's laws are defined for point particles, I'd like to derive some laws of motions for rigid bodies only by considering a rigid body as a system of particles such that the distances from ...
0
votes
0answers
36 views

Torque from Newton’s Laws

Is is possible to predict the motion of rigid bodies only in terms of Newton’s laws of motion without torque (for example by using the system of particles model)? For instance, if there was a rod of ...
2
votes
4answers
199 views

Helical motion of a rigid body

I want to show that a rigid body, with two components of its angular velocity vector and one component of its linear velocity vector, in the absence of external forces and torques, has helical ...
0
votes
3answers
59 views

What is the equation descriping a ball motion caused by non-perpendicular force?

What is the equation describing a ball motion caused by non-perpendicular force? For example in the next diagram F1 is perpendicular force but f2 is non-perpendicular force which I am asking about
1
vote
1answer
29 views

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 ...
0
votes
0answers
25 views

Goldstein expression derivation (Torque-free Motion of a Rigid Body)

In page 207 of Goldstein's "Classical Mechanics" (3rd edition) he writes the following expressions: I can't fully grasp how he was able to get to these expressions. I believe it has something to do ...
0
votes
1answer
67 views

How does tension work for a simple pendulum? What force is at play to keep a rigid body from stretching?

Here recently I have been working on programming a physics framework for simulations, but I've ran into a problem... I was testing forces, so I created a simple pendulum like in the photo, and I ...
0
votes
1answer
23 views

Directional cosines and rigid bodies

Suppose $Oxyz$ is fixed in space. We specify one reference point in the rigid body using Cartesian coordinates in $Oxyz$. We use this point as the origin of the body-fixed frame $O'x'y'z'$. Consider ...
0
votes
1answer
64 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\!\...
-1
votes
2answers
142 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?
0
votes
1answer
46 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 ...
10
votes
5answers
2k views

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 ...
2
votes
0answers
57 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}...
0
votes
0answers
14 views

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 ...
0
votes
1answer
68 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 ...
0
votes
0answers
60 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. ...
0
votes
0answers
15 views

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 ...
0
votes
1answer
53 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 ...
1
vote
3answers
46 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 ...
0
votes
0answers
30 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 ...
0
votes
1answer
59 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 ...
1
vote
2answers
99 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 ...
0
votes
1answer
54 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 ...
0
votes
1answer
28 views

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 ...
-1
votes
1answer
55 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.
0
votes
1answer
44 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 ...
1
vote
1answer
47 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 ...
1
vote
0answers
72 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 ...
1
vote
0answers
32 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 ...