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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Detecting absolute motion inside a box

This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows. ...
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232 views

Pendulum Hits a Mass and Spring

I think this problem’s solution is on the web but after a few days of searching, I can not find it. Can anyone give me a reference? Thanks in advance. A mass and spring are resting on a frictionless ...
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Strain energy density in index notation

The strain energy density is defined as $$dU = \int_0^{\epsilon_{ij}} \sigma_{ij} d \epsilon_{ij}$$ (see Reddy "Energy Principles and Variational Methods in Applied Mechanics", 2nd Ed, 4.11). Assuming ...
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How to derive energy expressions thinking of it as a conserved quantity only?

By now I understand that "energy is a conserved quantity" and that's all we need to know. Then, the idea of work comes as the change in kinectic energy of a system and we realise that having energy is ...
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291 views

Addes mass forces: can a force depend on acceleration?

My friend and I had a little discussion about added mass forces. I always interpreted "F=ma" as a cause-effect relationship, so I find rather uneasy to accept that the cause can instantaneously ...
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50 views

Find pressure of liquids without making contact with it

Is there any way to find the pressure of a liquid inside a closed container without making contact with it? You can make any assumptions, like transparent container or anything, only rule, the ...
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88 views

Derivation of Lagrangian?

I know that the Lagrangian $L$ is defined to be $T-V$, i.e. the difference between kinetic energy and potential energy. Also the Action $S$ is defined to be $\int Ldx$ and from this we can derive ...
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231 views

Potential energy from opposing magnets repelling each other with a gap of 1 mm

I have two powerful rare earth magnets, that are separated by a distance of 1 mm. I applied energy to bring them closer to each other, hence increasing the potential energy. Now, when one of the ...
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291 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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324 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: ...
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172 views

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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139 views

Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
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120 views

Mechanical shock resistance as a function of shape

I have a system where I'm dropping glass tubes filled with some sample from a certain height, along a track. I can apply a back-pressure of air to push them down faster, and in general the faster they ...
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1answer
38 views

Constant of motion

An exercise from Goldstein (9.31-3rd Ed) asks to show that for a one-dimensional harmonic oscillator $u(q,p,t)$ is a constant of motion where $$ u(q,p,t)=\ln(p+im\omega q)-i\omega t $$ and ...
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262 views

Atwood machine problem

Sorry for the bad drawing, but I hope that this will help you get a hold of the problem. Consider an Atwood Machine with a total of two blocks, a mass less pulley, ideal string. One block rests on ...
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1answer
229 views

How should a closed-ended terrestrial trajectory be corrected for the Coriolis effect?

I have tried verifying the numerical integration of the Coriolis effect for 1000 to 2000-yard rifle fire by switching ON/OFF the Coriolis correction of a good ballistic simulator program (PRODAS). The ...
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1answer
235 views

Additional accelerating force during take off of a rocket?

During the take off of a rocket, the exhaust produces some pressure below the rocket, which gives an additional force. How large is this force in comparison to the force produced directly by the ...
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1answer
37 views

Heuristic equation for Friction force between materials

I'm programming a game where different types of objects will be sliding over different types of terrains (Top-down in two dimensions). At my current level of physics education we are given the ...
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1answer
390 views

How to calculate the moment of inertia of a solid cube

How do I calculate the moment of inertia of a uniform solid cube about an axis passing through its center of mass? I also wanted to know if the moment of inertia ...
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1answer
146 views

Classical models with unbounded particle number

Is there any classical model which deals with the birth, life and death of particles? What application could it have? I am talking about a 'billiard-ball' kind of model, but the kind in which balls ...
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67 views

Universal gravity at small distance

Could it be that there is simply a maximum gravitational force that two bodies of finite mass can exert on one another? This would occur at $r=0$, so maybe there is some really really really small $a$ ...
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1answer
115 views

How do I figure out the momentum of a water balloon when it reaches the person I am throwing it at?

Recently an experiment was performed in which myself and a partner filled a water balloon and threw it back and forth at each other without breaking it. We gradually increased the distance at which it ...
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Could each non-dependent physical contant represent dimentions, and our universe be a point on this n-dimentional structure?

For example say the gravitation constant instead of equaling G, was actually a range bounded between 0 and infinity. Our Universe would be at a point on this range (equal to our G value) where ...
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Doubt in law of mutual interaction

Book: Classical mechanics (textbook) by Douglas Gregory (cambridge publications) Law of mutual interaction states that when two particle (let it be P1 and P2) interacts, the particle (P1) induces an ...
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358 views

Find generating function $F_1$ for canonical trasformation

I'd like to know the steps to follow to find the generating function $F_1(q,Q)$ given a canonical transformation. For example, considering the transformation $$q=Q^{1/2}e^{-P}$$ $$p=Q^{1/2}e^P$$ ...
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71 views

Rocket hovers- and then what?

If we have a rocket, using conservation of momentum we derived in my classical mechanics course $$m\dot{v}=-\dot{m}v_{ex}+F^{EXT}$$ $m$ is the total mass of the rocket and fuel still on the rocket ...
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45 views

Transformation of Hamiltonian in Sun-Earth System

In Sun-Earth system, what transformation law allows me to find the Hamiltonian H in an arbitrary inertial system knowing the same in the center of mass?
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52 views

A posteriori solution to the Hamilton Jacobi equation

I was wondering about the following: For many simple systems it is far too cumbersome to solve the Hamilton Jacobi equation compared with the Hamilton or Lagrange formalism. Now I was wondering, ...
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98 views

Problems at arriving on the fresnel drag coefficient $k=1-{1 \over n^2}$

I was studying about the Fizeau Water Experiment of 1851(I know the aether drag hypothesis has been replaced by Relativity, but I still wish to know the mathematical thinking about aether). So at one ...
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73 views

Practical examples or demonstrations similar to the Chaplygin sleigh

The Chaplygin sleigh is a simple nonholonomic mechanical system. The WP article is a fresh one that I just wrote based on a description by Bloch, and may contain mistakes. The first thing I thought ...
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122 views

Is the traditional free-body diagram invalid in situations in which equal forces produce unequal powers?

This question is in response to question B1 in the problems/solutions located at http://aapt.org/physicsteam/2013/upload/E3-1-7-solutions.pdf. In question B1, there is a wind-powered vehicle that can ...
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70 views

Relation between the period of rotation and the period of revolution of a satellite

I read somewhere that the tidal forces between the earth and the moon causes the equality between the 2 periods of the moon and that every planet-satellite system will evolve to this condition (like ...
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184 views

Dose the gravitational force produces precession in the spinning top?

I'm new at classical mechanics but the text book says there is the torque in the spinning top which generated only by gravitation. It is hard to explain the situation, I've add the link. ...
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334 views

How to calculate mechanical advantage of a worm gear?

How to calculate mechanical advantage of a worm gear? My textbook simply use the turn ratio as the mechanical advantage, but I'm not sure how that works. My thinking: If the worm has a radius of ...
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251 views

Maximum Shear on a Beam - beam with fixed support on one end and hinge on other end

A beam $\displaystyle 3m$ long with fixed support on one end and hinge on the other end is subjected to a uniform load of $10\ kN/m$. What is the maximum shear of this beam? The solution is this one: ...
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290 views

How to find angular velocity of a point inner a circumference

Let's consider a cicumference that have the center in the origin of axes and rotates around x-axes. Let's stick a bar in a point $A$ of this circumference and at the end of the bar let's stick a mass ...
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63 views

Finding an efficient strategy for walking

Let's say you are already walking at a maximally efficient combination of pace and stride (or $\omega$ and $X_0$ I guess) but you need to reach your destination faster. Should you increase/decrease ...
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References for circular restricted 3 body problem?

Does anyone know of any good references for the CR3BP -- the circular restricted 3 body problem? Emphasizing on real-life applications, and interpretation of the numerical solutions? Thank you. There ...
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874 views

Studying from “Berkeley Physics Course Volume I - Mechanics”

I'm a first year physics student and the main source for our Physics I course is "Berkeley Physics Course - Volume I." I'm having a hard time understanding this book because it assumes a pretty high ...