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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Generalized momentum conjugate and potential $U(q, \dot q)$

On Goldstein's "Classical Mechanics" (first ed.), I have read that if $q_j$ is a cyclic coordinate, its generalized momentum conjugate $p_j$ is costant. He obtained that starting from Lagrange's ...
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Question about de Broglie Waves?

Is photon interaction , electrostatic interaction outside the nucleus and gravitational interaction is all due to electromagnetic waves ? and CAN be identified as with the de Broglie waves ? I ...
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210 views

How do i choose a motor to power a one cubic metre cement mixer? [closed]

my problem is that I can’t find a way to calculate the power required to drive the shaft and thus decide on a motor, I have tried several times using different methods and calculations but can’t seem ...
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76 views

Is the geometric formulation of Hamiltonian mechanics really necessary? [duplicate]

Possible Duplicate: Why is the symplectic manifold version of Hamiltonian mechanics used in Newtonian mechanics? I was sitting around with some friends the other day trying to come up with ...
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Reference for the predictability of rigid body dynamics

I'm looking for a reference, journal article, paper, etc. that supports the idea that classical mechanics, in particular rigid body dynamics, is largely predictable. A view coming from the background ...
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650 views

To find whether a particle is in equilibrium or not

Actually the following question came in an exam i gave yesterday. I know the site does not allow home-work type questions, but as I am having a conceptual problem in solving the question, I am posting ...
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776 views

How accelerometers sense constant velocity movements

There is something I don't understand about accelerometers. I know it's possible to make an Inertial Measurement Unit (IMU) by using "three" accelerometers. So with that, I could calculate the $x$, ...
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418 views

By how much will water resistance and upthrust slows down a fully submerged object?

Consider the following example: While running, I do work and I have a certain velocity and acceleration. When I'm in a pool (my feet are touching the bottom), I do the same work but, I have less ...
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Determine the maximum height a pump can suck up water

I am working on a homework problem that presents the scenario of trying to raise water from a small reservoir of depth 8 m whose surface is 25 m below a pump that can maintain a pressure differential ...
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134 views

Non-relativistic Kepler orbits

Consider the Newtonian gravitational potential at a distance of Sun: $$\varphi \left ( r \right )~=~-\frac{GM}{r}.$$ I write the classical Lagrangian in spherical coordinates for a planet with mass ...
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489 views

How to explain the different forms of the Hamilton-Jacobi equation?

In Arnold's Mathematical Methods of Classical Mechanics, he derives the Hamilton-Jacobi equation (HJE) using a generating function $S_1(Q, q)$ to get $$ H\left(\frac{\partial S_1(Q, q)}{\partial q}, ...
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Obtaining point of application of Ground Reaction Force with use of a hyperstatic load-cell array platform

I'm looking for the theory of an experiment that is giving me a hard time to perform. I have an instrument composed of a rigid horizontal square plate rigidly supported under each corner by a ...
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When Hamiltonian and the total energy are the same

In which condition, the Hamiltonian is the same as the total energy of the system, or say $H=T+V$?
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Conservation of energy in objects at terminal velocities

In vacuum, object free falling under gravity, the sum of Gravitational Potential Energy(GPE) and Kinetic Energy (KE) is a constant. The GPE is a decreasing side of a quadratic and KE is a increasing ...
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The notion called aether

I am trying to learn relativity theory and going through an introductory text on special relativity. I stumbled on the Michelson-Morley experiment. The book claims (accounts) that the result of this ...
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Non-linear dynamics of classical hydrogen atom [duplicate]

Possible Duplicate: Non-linear dynamics of classical hydrogen atom I'd like to know if there have been attempts in solving the full problem of the dynamics of a classical hydrogen atom. ...
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280 views

Non-linear dynamics of classical hydrogen atom

I'd like to know if there have been attempts in solving the full problem of the dynamics of a classical hydrogen atom. Taking into account Newton equations for the electron and the proton and Maxwell ...
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237 views

Clarification on a Goldstein formula steps (classical mechanics)

At page 20 of Classical Mechanics' Goldstein (Third edition), there are these two steps given between eqs. (1.51) and (1.52): $$\sum_i m_i \ddot {\bf r}_i \cdot \frac{\partial {\bf r_i}}{ \partial ...
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What are the fields in this problem?

In problem 3 of chapter 2 of Landau Lifshitz "Mechanics," I don't understand the meaning of the fields as defined in the following statement: Which components of momentum and angular momentum are ...
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969 views

Is it reasonable for a heavy door to “open by itself” (ie from differences in air pressure) if it had already been slightly ajar?

If you consider a basically uniform massive door (say, 300 N) where there is some coefficient $\mu_{s,k}$ of static and kinetic friction between the thing on the inside of the door, and where the ...
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Landau Mechanics: why does adding Lagrangians remove the indefiniteness of multiplying each Lagrangian by a different constant?

In Landau Mechanics (third edition page 4), why does adding Lagrangians of two non interacting parts remove the indefiniteness of multiplying each Lagrangian by a different constant? If both systems ...
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330 views

Can I find a potential function in the usual way if the central field contains $t$ in its magnitude?

I'm working on a classical mechanics problem in which the problem states that a particle of mass $m$ moves in a central field of attractive force of magnitude: $$F(r, t) = \frac{k}{r^2}e^{-at}$$ ...
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Coriolis force in free fall

Does the coriolis force has any measurable effect in free fall from large heights? Take for example the sky diving experiment by F. Baumgartner who started from a height of about 40 km above New ...
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What are the reasons for leaving the dissipative energy term out of the Hamiltonian when writing the Lyapunov function?

I have a problem with one of my study questions for an oral exam: The Hamiltonian of a nonlinear mechanical system, i.e. the sum of the kinetic and potential energies, is often used as a Lyapunov ...
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3k views

What is the relationship between mass, speed and distance of a planet orbiting the sun?

After reading this fascinating story about a new exoplanet, I was wondering about how mass, speed and distance determine a circular orbit of a planet around a star. Given the mass of the sun and ...
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883 views

Charge, velocity-dependent potentials and Lagrangian

Given an electric charge $q$ of mass $m$ moving at a velocity ${\bf v}$ in a region containing both electric field ${\bf E}(t,x,y,z)$ and magnetic field ${\bf B}(t,x,y,z)$ (${\bf B}$ and ${\bf E}$ are ...
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Differences between classical, analytical, rational and theoretical mechanics

Can you explain me what are the differences between the four following subjects? analytical mechanics rational mechanics classical mechanics theoretical mechanics
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Stacking gold Bars

I once heard that because gold is so malleable, while also being very heavy; that if one were to stack several layers of bars on top of on another (like is so familiarly depicted in movies & TV), ...
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The Z-Torque: how can it be shown intuitively that it does not work?

There is a new kickstarter project that claims to increase torque and power compared to a normal crank on a bicycle (Z-Torque on kickstarter). If this patented (US Patent Number 5899119) approach ...
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172 views

Problem in Hamiltonian

I need to elaborate the equation ,and need to know what is the physical significance and how matrices will manipulate in the equation $$ \hat{H} = (\hat{\tau_3}+i\hat{\tau_2})\frac{\hat{p}^2}{2m_0}+ ...
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378 views

Determining friction for unbalanced wheel to roll without sliding

I'm trying to model a weighted wheel rolling without slipping. I understand that friction, by virtue of being an off-center force, affects both linear and angular acceleration. So my train-of-thought ...
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Do strong and weak interactions have classical force fields as their limits?

Electromagnetic interaction has classical electromagnetism as its classical limit. Is it possible to similarly describe strong and weak interactions classically?
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Particles as a limit of classical field theory

A common academic exercise has been to show that classical mechanics is a limit of quantum mechanics, usually by putting $\hbar \rightarrow 0$. Similarly is it possible to show that a limit to field ...
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Is it possible to find out the distance traveled by a car if the force applied on it is given?

Say you have car which produces $F$ amount of force which is transferred to the wheels directly. Now assuming that there is air friction which is causing a retarding force proportional to the ...
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Physics behind Wheel Slipping

Lets say that I'm in a car and I apply full acceleration suddenly. Now, the wheels would slip and hence the car doesn't displace much. But If I start with some constant acceleration, slipping doesn't ...
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Reference request: Classical Mechanics as an Application to Smooth Manifolds [duplicate]

Possible Duplicate: Classical Mechanics for Mathematician Last time I asked a question, but it does not sound specific. I am currently taking graduate topology class (using Lee's ...
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Microphones, Loudspeaker and their analogies to spring mass system

I have just started studying Microphones and Loudspeakers. I need a good text to refer which can explain their mechanical analogies with simplicity and basics too.
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Determining the center of mass of a cone

I'm having some trouble with a simple classical mechanics problem, where I need to calculate the center of mass of a cone whose base radius is $a$ and height $h$..! I know the required equation. But, ...
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Eternal clocks and 4D spacetime crystals

There was a recent article about the creation of 4D spacetime crystals based on recent theory proposed by Frank Wilczek. This theory is based on breaking time translational symmetry which basically ...
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130 views

Physics of homebrewing heat exchangers

In homebrewing on of the key steps when brewing with extract is to rapidly chill the wort from boiling temperatures to about 80F in 30 min. This is needed to reduce risk of environmental ...
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What's driving the bucket up?

Just saw this cool video from Plymouth University, which I actually found through Matthen's blog. They fill a plastic bottle with liquid nitrogen, screw the cap on, drop it in a bucket full of warm ...
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181 views

Rigid body/moment of inertia problem

I have a homework assignment about rigid body dynamics. Take a disc of radius $r=2m$ with uniform mass density $\rho=1$ $kg/m^2$ in the x-y plane, resting in an inertial frame. At some instant, a ...
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Meaning of subscript in $V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$

This is probably a simple question, but what does the subscript $0$ mean in the following expression? $$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$
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If a people happen to be fall into the ocean from 50m high, then would the diving pose in the olympiad make less percussion

If a people happen to be fall into the ocean from 50m high, then would the diving pose in the olympiad make less percussion then the leg going first into the water so that the body receive less ...
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Is the principle of least action a boundary value or initial condition problem?

Here is a question that's been bothering me since I was a sophomore in university, and should have probably asked before graduating: In analytic (Lagrangian) mechanics, the derivation of the ...
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483 views

Hamiltonian Flow Map

I'm reading this article and am struggling with some of the terminology. What is the flow map for a Hamiltonian system? I'm looking for a rigorous definition really! Many thanks in advance.
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395 views

What shape of track minimizes the time a ball takes between start and stop points of equal height?

I was at my son's high school "open house" and the physics teacher did a demo with two curtain rail tracks and two ball bearings. One track was straight and on a slight slope. The beginning and end ...
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Deriving the action and the Lagrangian for a free point particle in Special Relativity

My question relates to Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action. As stated there, to determine the action ...
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Centrifugal Force and Polar Coordinates

In Classical Mechanics, both Goldstein and Taylor (authors of different books with the same title) talk about the centrifugal force term when solving the Euler-Lagrange equation for the two body ...
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Mechanics Energy (Calculus)

A particle moves with force $$F(x) = -kx +\frac{kx^3}{A^2}$$ Where k and A are positive constants. if $KE_o$ at x = 0 is $T_0$ what is the total energy of the system? $$ \Delta\ KE(x) + \Delta\ ...