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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Nature of orbit due to central force! [duplicate]

Possible Duplicate: Kepler problem in time: how do two gravitationally attracting particles move? How do we get the shape of orbit under the condition that Force is centrally directed ...
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224 views

Why doesn't relativistic momentum appear conserved in this frame?

Suppose I have an inelastic head on collision between two idential particles of mass $m$ that come to rest in the centre of momentum frame where relativistic momentum is obviously conserved. If I now ...
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149 views

What's the amount of deviation of cellestial orbits from perfect ellipses

It's well known that the planets don't orbit the sun in perfect circles and the characteristics of the elliptical orbits which serve as better approximations to their motion have been calculated ...
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617 views

Why are coordinates and velocities sufficient to completely determine the state and determine the subsequent motion of a mechanical system?

I am a Physics undergraduate, so provide references with your responses. Landau & Lifshitz write in page one of their mechanics textbook: If all the co-ordinates and velocities are ...
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23 views

On Bolte's semiclassical law

i have seen on internet the following, for $ E >> 1 $ the Eigenvalue Staircase can be approximated by $ N(E)= \frac{1}{\pi}argZ(1/2+i \sqrt E ) $ ...
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How to determine an exponential acceleration curve?

I've always been not so bad in mathematics, but I'm terribly bad at physics. For me, abstract concept are totally understandable, but when it come to reality, I'm lost ! So, for my job, I need to ...
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101 views

Rotationally invariant body and principal axis

Suppose a rigid body is invariant under a rotation around an axis $\mathsf{A}$ by a given angle $0 \leq \alpha_0 < 2\pi$ (and also every multiple of $\alpha_0$). Is it true that in this case the ...
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707 views

Cases in which angular velocity and angular momentum point into same direction

I know that angular momentum $\vec{L}$ and angular velocity $\vec{\omega}$ of a rigid body doesn't point into the same direction in general. However if your body spins around a principal axis, ...
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Why Liouville's theorem is obvious?

In Florian Scheck's Mechanics, he stated the local form of Liouville's theorem as follows: Let $\Phi_{t,s}(x)$ be the flow of the differential equation $-J\frac{d}{dt}x=H_{x}$. Then for all $x,t,s$ ...
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2k views

Rubber Band Forces

I have a question regarding the force a band places on an object. Say I have a rubber band wrapped around 2 pegs at a certain distance, and at that distance I know the pounds of force per inch it is ...
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267 views

Why $\frac{d}{dt}r_{a}\nabla_{a}U_{ab}+\frac{d}{dt}r_{b}\nabla_{b}U_{ba}=\frac{d}{dt}U_{ab}?$

In classical mechanics for two mass particles $a$,$b$ we assume the symmetric potential arising from $F_{ab}$ and $F_{ab}$ given by $$U_{ab}(r)=-\int^{r}_{r_{0}}F_{ab}(r')dr'$$ and ...
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160 views

Say we're driving a bike and suddenly hold the brakes?

It's easy for me to imagine that if we brake the front wheel then there is a chance that I'll flip. On the other hand if I brake the back wheel, there is no way it'll happen no matter how fast I ...
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Has any permanent magnet motor been proven to run?

I have read lots of articles about permanent magnet motors, some of which claim the possibility and other which refute it. Is it possible to have a permanent magnet motor that runs on the magnetic ...
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330 views

Numerical torque calculation

Suppose I can compute interaction energy of two rigid bodies as a function of their coordinates of centers of masses and Euler rotation angles (total 6 + 6 degrees of freedom). Now I can numerically ...
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2answers
164 views

Linking two balls together

I have a physics simulator that simulates a bunch of balls moving and colliding with each other, and I would like to be able to "link" two balls together so they stick to each other (are always ...
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Why do we need the quantity momentum?

Why do we need the quantity Momentum in physics when we have the quantities like Force and Energy? Isn't it possible to substitute the usage of Momentum with equivalent of Force and Energy?
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1answer
530 views

How does a star wobble due to orbiting bodies

What equations determine how a star wobbles in response to an orbiting planet, and can it be used to determine the mass of distant objects based on the wobble? If there are other more reliable ...
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2answers
2k views

Conservation of angular momentum in helicopter

I have a small RC-controlled toy helicopter with removable tail rotor. Suppose I remove the tail rotor, hold the tail with my hand, start the rotor until it moves with constant angular velocity and ...
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1answer
349 views

How to determine n equidistant vectors from point P in three dimensions

As an assignment for uni I need to figure out an algorithm that explodes a particle of mass $m$, velocity $v$, into $n$ pieces. For the first part of the assignment, the particle has mass $m$, ...
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18k views

Difference b/w Kinetics & Kinematics w/concrete example

(I know whether I understand this or not doesn't matter much to my work & study but am just curious.) I still can't differentiate in my head kinetics and kinematics (similar thread is found but ...
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Can a force in an explicitly time dependent classical system be conservative?

If I consider equations of motion derived from the pinciple of least action for an explicilty time dependend Lagrangian $$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$ under what ...
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1answer
357 views

Will a precessing spinning wheel fall down if there is no friction at all?

If there where no friction at all, would a spinning wheel held up by one end of the axis spin precess forever without falling down? I just asked another question about the same problem: Direction ...
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Direction of torque precession of a spinning wheel

Consider a spinning wheel, which is held up by one end of it's axis like this: To explain why the change of angular momentum is directed as shown in the figure above, one usually says that there is ...
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1k views

How to interpret this vertical circular motion problem?

A bucket of water is tied to a rope and swung in a vertical circle. The distance from the bucket centre to the axis of rotation is $2.08m$. Calculate the angular velocity (in $rad s^{-1}$) of ...
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467 views

What techniques can be used to analyze a rod rotating about the edge of a table?

A uniform rod of length $4x$ is rotating about the edge $O$ of the table. (The rod does not fall off the table.) The centre of mass $G$ of the rod is distance $x$ away from $O$. The rod is making ...
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Normal force in a compound pendulum (physical pundulum) system?

Consider a compound pendulum pivoted about a fixed horizontal axis, illustrated by the force diagram on the right: # Okay, I can't figure out where the normal force on the pendlum should point ...
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873 views

Calculate relativistic boost to COM frame from two arbitary velocities?

Looking in Goldstein's book, there doesn't seem to be a standard formula to calculate the COM frame velocity for two particles, from their relativistic velocities in the lab frame, although it is done ...
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2answers
536 views

What sustains a rigid body's rotation at its constant angular(rotational) speed?

Continuing from the following scenario from my previous question Centripetal force of a rotating rigid body? : Consider someone pushing a roundabout in a playground. Initially the roundabout is ...
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236 views

Why aren't stratospheric balloons compressing their helium to descent? [closed]

I can't find a reference of a working stratospheric balloon mounted with a compressor to control its altitude. Is there a big physical difficulty (such as compressor weight/power ratio, or power ...
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326 views

moment of tennis racket & volley

I've been looking for the relation between moment of a tennis racket and its maneuverability. If I define maneuverability as the easiness to get in position for quick reaction strokes like volleys and ...
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2k views

Would this model of a boat move according to Newtons 3rd Law?

If i have a small toy boat with a sail, and i attach a fan onto it, FACING THE SAIL, which runs by solar. Once the fan turns on will the boat move or will it remain at rest. Apparently it wont because ...
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1answer
106 views

understanding the oscillating part of the Gutzwiller trace

given the density of states according to Gutzwiller's trace formula $ g(E)= g_{smooth}(E)+ g_{osc}(E) $ i know that the 'smooth' part comes from $ g_{smooth}(E)= \iint dxdp \delta(E-p^{2}-V(x)) $ ...
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2answers
14k views

What is the exact definition of center of gravity?

I've come across many definitions. Is it 1) The point from which the weight of the body acts, i.e., the point at which if the entire mass of the body is assumed to be concentrated, the gravitational ...
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Why do non-Newtonian fluids go hard when having a sudden force exerted on them?

You can dip your hands into a bowl of non-Newtonian fluid but if you are to punch it, it goes hard all of a sudden and is more like a solid than anything else. What is it about a non-Newtonian fluid ...
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321 views

How do I visualize the non-coaxial rotation of this device?

The picture below shows an isolated system with a fairly massive wheel at one end, attached via its axle to a long shaft, like a bike tire on a bike frame, but the bike frame is merely a low mass ...
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1answer
258 views

two pendulums, which pendulum has shorter period [duplicate]

Possible Duplicate: A pendulum clock problem There are two pendulums. First pendulum consists of a rod of length L and flat heavy disk of radius R (R < L), disk is connected rigidly to ...
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1answer
814 views

Can relativistic kinetic energy be derived from Newtonian kinetic energy?

Relativistic kinetic energy is usually derived by assuming a scalar quantity is conserved in an elastic collision thought experiment, and deriving the expression for this quantity. To me, it looks ...
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2answers
136 views

sending information over a wire--mechanically [duplicate]

Possible Duplicate: Is it possible for information to be transmitted faster than light? I've thought about this since I was a little kid. I know it isn't exactly feasible, but it still ...
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1answer
476 views

Maximum speed of a water skier

Water skiing is a sport where an individual is pulled behind a boat or a cable ski installation on a body of water, skimming the surface. Consider an idealized case where the boat is moving at a ...
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164 views

Functional determinant approximation

Let the Hamiltonian in one dimension be $H+z$, then I would like to evaluate $\det(H+z)$. I have thought that if I know the function $Z(t) = \sum_{n>0}\exp(-tE_{n})$ I can use $$\sum_{n} ...
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2answers
827 views

Is the change in kinetic energy of a particle frame independent?

Intuitively, I would expect the change in kinetic energy of a particle to be frame independent. It just doesn't "feel" right that between two points in time-space, one frame should measure a change in ...
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1answer
532 views

The form of Lagrangian for a free particle

I've just registred here, and I'm very glad that finally I have found such a place for questions. I have small question about Classical Mechanics, Lagrangian of a free particle. I just read Deriving ...
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1answer
105 views

Orbits for space missions

I am just wondering say if there is an expedition where some astronauts are sent to the moon, how do they choose the trajectory for the spaceshuttle (or whatnot)? I mean there are many possible ...
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1answer
282 views

A question regarding particle trajectories in the symplectic manifold formalism

How to solve a free particle on a 2-sphere using symplectic manifold formalism of classical mechanics ? Is there a way to get coriolis effect directly, without going into Newton mechanics? And is ...
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1answer
1k views

Classical Mechanics for Mathematician [duplicate]

Possible Duplicate: Which Mechanics book is the best for beginner in math major? I am looking for suitable ways to learn mechanics in mathematician's perspective. I went through: ...
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3answers
4k views

Deriving the Lagrangian for a free particle

I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading "Mechanics" by Landau and Lifshitz recently and hit a few roadblocks right away. Proving that a free particle ...
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1answer
598 views

A Question about Virtual Work related to Newton's Third Law

In describing D'Alembert's principle, the lecture note I was provided with states that the total force $\mathbb F_l$ acting on a particle can be taken as, $$\mathbb F_l=F_l+\sum_mf_{ml}+C_l,$$ ...
3
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2answers
177 views

Does locality emerge from (classical) Lagrangian mechanics?

Consider a (classical) system of several interacting particles. Can it be shown that, if the Lagrangian of such a system is Lorenz invariant, there cannot be any space-like influences between the ...
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469 views

When “unphysical” solutions are not actually unphysical

When solving problems in physics, one often finds, and ignores, "unphysical" solutions. For example, when solving for the velocity and time taken to fall a distance h (from rest) under earth gravity: ...
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How do levers amplify forces?

This is really bothering me for a long time, because the math is easy to do, but it's still unintuitive for me. I understand the "law of the lever" and I can do the math and use the torques, or ...