# Tagged Questions

Classical mechanics refers to the classical (i.e., non-relativistic, non-quantum) study of physics. Three major formulations of classical mechanics are newtonian mechanics, lagrangian mechanics, and hamiltonian mechanics. The latter two are rather useful in extensions to Classical Mechanics; ...

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### Non-canonical transformation

I would like to know any method to transform a known non-canonical set of variables to a canonical set for a given system. The Lagrangian and Hamiltonian are known in the non-canonical variables. I ...
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### Note and homework organization [closed]

I am currently in a mechanics class and have some trouble trying to figure out how I should structure my lecture notes and my homework. I recently began rewriting my notes after class but I am still ...
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### Could a “living planet” alter its own trajectory only by changing its shape?

In Stanislaw Lem's novel Solaris the planet is able to correct its own trajectory by some unspecified means. Assuming its momentum and angular momentum is conserved (it doesn't eject or absorb any ...
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### Experimental data for asymmetric Newton cradle

Using a "successive impact model" (as if each ball were seperated from the other ones), I produced the following animations: You can see any combination of balls with masses of 1 or 2 (left) or 1 ...
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### Fragmentation of a curved cantilever beam under compression [migrated]

Suppose we have a curved beam of a rectangular cross-section A, reduced modulus E, and a constant radius of curvature R. We now expose the beam to a compressive point load of magnitude P at its free ...
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### Airplane on a treadmill - Variant Thought Experiment

This thought experiment is in a way related to the (in)famous airplane on a treadmill problem. If you take a ball and place it on a treadmill, will the ball: Move backwards relative to the ground ...
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### Consistent method for finding direction of static friction

I am having trouble coming up with a consistent method of determining the direction of static friction. So far the best I have come up with is: it should oppose the relative acceleration the contact ...
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### Comparison of velocity Verlet and leapfrog algorithms [migrated]

Many sources present the Euler, Verlet, velocity Verlet, and leapfrog algorithms for integrating Newton's equations. Based on the order of accuracy, it is agreed that velocity Verlet, Verlet, and ...
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### what is the physical meaning of area moment of inertia?

In our applied mechanics class, we studied about area moment of inertia. Our teacher only explained the mathematical relation of this term that is product of area and square of the perpendicular ...
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### Salt in a pot of water [duplicate]

I noticed that when I throw salt into a cooking pot and then mix, the salt collects in the center. As salt is denser than water, I would have expected it to go towards the border of the pot, and not ...
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### Why do we use orthogonal axes?

I have been asked several times that “why do we use orthogonal axes in coordinate systems?” and I was always replying that “because of simplicity”. But, today morning, someone asked me that question ...
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### Electric Field under Time reversal

We know under time reversal electric field does not change direction. I am doubtful about it. Imagine an electric field parallel to x-axis (in positive x direction) and a charge moving parallel to ...
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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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### 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,...
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### Reference Request: Classical Mechanics with Symplectic Reduction

I am trying to find a supplement to appendix of Cushman & Bates' book on Global aspects of Classical Integrable Systems, that is less terse and explains mechanics with Lie groups (with dual of Lie ...
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### Why does the period of a pendulum decrease in an accelerating frame? [duplicate]

If there is a simple pendulum in a non-accelerating frame with period $T_1$, it will have period $T_2 < T_1$ when placed in a frame accelerating perpendicularly to the direction of gravity. Why?
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### Lagrangian of an effective potential

If there is a system, described by an Lagrangian $\mathcal{L}$ of the form $$\mathcal{L} = T-V = \frac{m}{2}\left(\dot{r}^2+r^2\dot{\phi}^2\right) + \frac{k}{r},\tag{1}$$ where $T$ is the kinetic ...
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### What are the mathematical models for force, acceleration and velocity?

In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
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### Relation between field and Potential energy of a body

I have read that if a body is in a field and is 1. moved in a direction opposite to the direction of a field, its potential energy increases.But why does it increase? 2.Also, if we move the body in a ...
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### Collision/Crumpling problem possible solution mistake

This question is from Physics for scientist and engineers , Ohanian . Two automobiles of 540 and 1400 kg collide head-on while moving at 80 kmh in opposite directions. After the collision the ...
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### Integrals of motion for a free particle

I'm struggling to understand the argument on p. 13 in Landau and Lifshitz that for a system with $N$ degrees of freedom there must be $2N-1$ integrals of motion. In particular, I can't understand ...
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### Difference between naive and Coriolis-force calculation

Consider the classical problem of dropping a coin from a tower at the equator of a planet without atmosphere and with spin $\Omega$: where in relation to a plumb-line will the coin land? When doing ...
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### How does a lever magnify force? [duplicate]

I understand that energy is conserved when a force is applied to the end of a lever and magnified closer to the pivot point. However, I would like to know how it is the force is transferred and ...
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### Explanation of force amplification inside a solenoid

For a system being actuated by a motor, the force can be amplified by gearing. The energy is being used for force instead of distance, so it produces more torque but moves slower. For a system being ...
(Apologies if HW questions are not allowed -- I couldn't really find a definite answer on this) Question Let $Q^1 = (q^1)^2, Q^2 = q^1+q^2, P_{\alpha} = P_{\alpha}\left(q,p \right), \alpha = 1,2$ ...