# Tagged Questions

A tag for questions about the mechanical interactions of rotating objects, including torque and angular momentum.

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### How can I approximate Jacobian Elliptic Functions in terms of basic integrable functions for the 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 showed in f.ex. this paper, ...
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### Bottle stability optimization

A few days ago some friends and I played a game called "flunkeyball" where you need to upset a bottle with a ball. Then a question occurred: "How much water do we need to put into the bottle that its ...
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### Why does the video recorded by a falling, rotating camera seem to stabilize?

Here is a video of a GoPro falling from a plane: http://www.youtube.com/watch?v=QrxPuk0JefA Any idea what is happening when the image "stabilizes" around 0:35? I think it is because the camera's ...
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### Gimbal Lock: why is it a problem?

I was watching this video http://www.youtube.com/watch?v=rrUCBOlJdt4 about the gimbal lock problem. I understood that during rotations it could happen that one DOF disappear. Looking at the middle ...
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### Rotating a Gaussian Beam

I need to see how the phase fronts of two gaussian beams interact when they intersect with each other. The two beams are tilted towards each other so that they intersect each other at their respective ...
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### Difference of the O(N) Non-linear Sigma model and SO(N) Non-linearSigma model

The Hamiltonian $$H=J\sum_{i,j}\vec{n}_i\cdot\vec{n}_j$$ is invariant under a global rotation $\vec{n}_i\rightarrow R\vec{n}_i$, where $\vec{n}$ is a $N$ component rotor ...
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### 3 Axis Gryroscope with forced Precession and Limits of Motion

I am working a problem concerning a 3 axis gryoscope, the spinning mass is a magnet (dipole). This is part of a optical sensing device. The inner gimbal is for pitch rotation, and the outer gimbal is ...
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### Videos of changing the orientation of an astronaut in space

Kane, Headrick and Yatteau describe in their paper "Experimental investigation of an astronaut maneuvering scheme" possible maneuvers to change the orientation in space without external torque. Is ...
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### Forces and torques about the CENTER OF MASS of a physical pendulum

I'm currently stumped by the following situation. Say we've got a rectangular physical pendulum (think ruler with a hole-punch at one end). It's trivial to analyze the motion of the pendulum with the ...
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### To prove uniqueness of the rotation tensor associated with rotation of a rigid body

Suppose there are $N$ particles embedded in a rigid body which undergoes some random rotation such that: $$\overline{\overline {R}}_{ij} \otimes \vec{a}_{ij} = \vec{b}_{ij}$$ where, $i$ and $j$...
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### Does a potential of interaction produce also torque?

I have a system of particles (spheres with masses and radii), with $6$ degree of freedom (they are free to move and rotate as they wish). Between each couple there is an interaction potential $V(d)$, ...
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### Simple powertrain dynamics

I'm trying to simulate vehicle powertrain and having problems at calculating correct impulse at the wheel. Here's what I have. Gear Ratio There are two gear ratio in the system $N_g$: ...
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### Angular Momentum

I have several questions about angular momentum. 1.I know there are 2 parts of angular momentum - translational and rotational. For a body with respect to a fixed point, translational angular ...
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### Uranus, the Physical model to change it's rotation axle

Uranus rotates pretty wierd, it's 90-degrees tilted; Why is Uranus's axis of rotation tilted? The best answer for this is; that at a distant point in its past, Uranus was struck by a very ...
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### integrating small angular velocities

I know that for a constant angular velocity the following is true: $R=e^{W t} R_0$ where $W$ is an angular velocity tensor, $t$ is a time, and $R$ is a rotation matrix I believe the following is ...
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### Solving for position of a SO(3) rotating object, given the integrable functions for components of angular velocity along the principle axes

Assuming that you have approximated or solved the Euler's Equations for components of angular velocity along its principal axes of inertia $x$, $y$ and $z$ - i.e. in the coordinate system that is ...
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### Rotational dynamics equation for a variable mass system?

I'm searching for the formulation of Euler's rigid body dynamics in the case of a variable mass system. I'm reading the book Mechanics of Flight by Warren F. Phillips (2nd edition) and unfortunately ...
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### Rotational Spectrum of a Diatomic Molecule

The rotational energy levels of a diatomic molecule are given by $$E_l=\frac{\hbar^2}{2I}l(l+1)$$ where $l$ is an integer. If the molecule is a dipole it can emit or absorb electromagnetic radiation ...
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### Name for the transformation into an accelerated frame?

A transformation into a frame that looks at an experiment from a rotated perspective is called a rotation. A transformation into a frame that moves with a different constant velocity is called a ...
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### Gears in contact?

I was doing a practice exam paper question that was along the following lines: A gear, $A$,and moment of inertia $I_A$ is spinning about its axis at angular velocity $\omega$. Another gear $B$ (...
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320 views

### Torsion Spring Moment Calculation

I'm trying to extend the idea of a translational spring to a rotational spring. Consider a spring that acts on all displacements of a body:  \mathbf{F} = \begin{bmatrix} F_x \\ F_y \\ F_z \end{...
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202 views

### Friction and work from torque

I would like to understand where is the error in the third case, for that I gave 2 easier cases where I'm able to find the energy from heating is equal to the energy lost by torque. Case 1/ Purple ...
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### Moment of inertia about a tilted axis

I apologize if it seems foolish, I am a beginner. Suppose I am given an object, whose moment of inertia along the x,z axes are known. Suppose it rotates around a tilted axis, ...
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### Magnetic field of solenoid in cone shape

I have done some drawings of the magnetic fields of cone shaped solenoid electromagnets. I based this on the work of Tesla and some explanations of Bashar, known as the Bashar Cones. I found very ...
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### Why does angular velocity lies in the axis passing through the center of the circumference?

I understand that it can't be placed anywhere on the radius because it doesn't vary with it ( and so of course it doens't make sense to place it anywhere else on the plane), but why do we place it ...