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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...
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: ...
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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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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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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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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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, ...