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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Independence of generalised coordinates and momenta in Hamiltonian mechanics [duplicate]

I am told that in Hamiltonian mechanics, we put the generalised coordinates $q_i$ and generalised momenta $p_i$ on equal footing, and treat them as being independent from one another. But I'm ...
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132 views

Mathematics of the Virtual Displacement

So I'm pretty certain this question has been asked to death here, but I still can't find a good explanation of a very particular aspect of the virtual displacements in physics. Background For ...
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102 views

Find the separation distance for a line of oil being squashed between two flat plates [closed]

I was wondering if someone could give me some help on how to start this problem, I'm really struggling to get my head around it. A long line of oil is being squashed between two flat plates of length ...
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153 views

What was the motivation behind the work formula?

Surely there must be a reason we decided to use this as a metric for mechanical energy.How was it developed and what made it more acceptable than other work formula candidates (Like force over time, ...
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99 views

For infinitesimal Canonical Transformations, what functions are allowed for this to be a canonical transformation?

Consider two infinitesimal transformation: $$q_{i} \rightarrow Q_{i} =q_{i} + \alpha F_{i}(q,p) $$ $$p_{i} \rightarrow P_{i} = p_{i} + \alpha E_{i}(q,p) $$ where $α$ is considered to be ...
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165 views

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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2answers
170 views

Composing integrals in physics?

OK... so this problem isn't really specific... it's more of a conceptual puzzle. I've recently started using integrals while solving problems in physics (specifically Newtonian Mechanics and other ...
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146 views

What is the classical counterpart of an eigenstate?

Does this question make sense for every system or just some? If it makes sense, it is a periodic orbit?
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108 views

Partition function of a 3D vibrating string

Is the partition function of a 3D vibrating string a sum of discrete energies, an integral of an energy continuum, or both? $$ Z_{\text{disc}} = \sum_{k=1}^{\infty}g_ke^{-\beta E_k} $$ or $$ Z_{\text{...
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48 views

Why is a bending rod assumed to be undergoing torsion?

If I take a rod and bend it at both ends as far as it will go, why is there an assumption that I am also exerting a torsion along with my bending? Referencee: ccording to the third edition of "Theory ...
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97 views

Equations of motion for a system of $n$ particles given the potetial [closed]

I am having difficulties on the following question: The equations of motion for a system of n particles are: $$m \ddot{x}_i = - \dfrac{\partial U(x_1,...,x_n)}{\partial x_i}$$ $$\ddot{x}_i = \...
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749 views

Mechanical equilibrium : thermodynamics and classical mechanics

A similar question was asked here but mine is a bit different. In thermodynamics, a mechanical equilibrium is defined as a uniform pressure (for a fluid). In classical mechanics, equilibrium is ...
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127 views

Determining the components of the force on a curved surface due to pressure

I have a cross section of a half-tube with a pressure gradient across it causing a force outwards. I am attempting to extract the vertical component (in relation to diagram) of the force on this semi-...
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33 views

Motion in a central field in Landau Mechanics

What does this mean when E=U_eff? I don't think this means the first term in E is zero. I don't understand the sentence ' This is a cubic equation for cos(theta)'
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72 views

Classical Hydrogen Atom

I was wondering about the Hamiltonian description of the classical hydrogen atom (two point particles interacting through a Coulumb potential). In particular, I want to know if the fact that ...
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271 views

One force applied to one point of a rigid body: centre of mass and torque [duplicate]

Let us suppose that one force is applied to a point of a rigid body that is not acted upon by any other force. I think an example can approximatively be a rock in deep space, far from any relevant ...
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76 views

Continuity Equation for Momentum

Momentum is a conserved quantity, which makes me wonder if we can write an equation for the local conservation of momentum in the form of a continuity equation. If we're considering a system of ...
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82 views

Lagrangian formalism (demonstration)

My question is about the multiplicity of the Lagrangian to a Physics system. I pretend to demonstrate the following proposition: For a system with $n$ degrees of freedom, written by the ...
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170 views

Hamilton-Jacobi theory and initial value problem?

Having read through some recent posts regarding the Lagrangian formulation being interpreted into an initial value problem rather than the familiar boundary condition problem we are familiar with, I ...
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93 views

Energy drain in damped oscillator

Suppose we have a mass on a spring with a damping term. The equation of motion is given by: $$m \ddot{x} = -kx - c\dot{x}$$ I believe solutions are damped oscillations of the form: $$x = x_0 e^{-\...
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64 views

Is the force of a lifting arm due to a piston an internal force?

When I was analyzing an excavator, I was wondering if the force that the piston exerts on the lifting arm is an internal or external force. I am a bit confused because the geometry of the system ...
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125 views

Why ingoing and outgoing impact parameters equal in elastic scattering?

Take the Rutherford scattering, as for example in this picture: What is the easiest way to show that the impact parameter "b" (see picture) is the same for the ingoing and outgoing trajectories? ...
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45 views

Acceleration in a system equal for every body — why?

A 1 kg cart can slide frictionlessly on the table. The black weights each weigh 1 kg. The pulleys are frictionless. The task is to determine the acceleration of the cart. For the left-most weight we ...
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259 views

Why does this ball have potential energy at its lowest point?

A ball of radius $r_0$ starts from rest at point $A$ on the inside of a track of radius $R_0$. The question is what will its speed be when it reaches the lowest point of the track, point $B$, assuming ...
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498 views

Find angular velocity of motor

I'm quite bad at this, but I'm trying to change that and I need some assistance. Please bare with me while I attempt to explain what I'm trying to figure out and correct me where I'm wrong. Basically ...
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220 views

Star vibration frequency due to gravitation

I found the following problem on a Classical Mechanics MIT problem set, which is intended to be solved by dimensional analysis: Derive an expression for the vibration frequency of a star of mass M ...
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322 views

Work done: kinetic energy or area under F-ds curve?

Starting from $$F=ma = m \frac{dv}{dt} = m \frac{ds}{dt} \frac{dv}{ds} = m v \frac{dv}{ds}, $$ leads to work done = integral of F.ds = integral of mvdv = change in KE. Suppose a variable force is ...
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106 views

Is trajectory the same as an orbit?

Is trajectory the same as an orbit? I wanted to know about gravity assists, but most books I find are talking about different types of orbits and such. Are they related?
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482 views

Why are position and velocity enough for prediction and acceleration is unnecessary?

In classical mechanics, if you take a snapshot and get the momentary positions and velocities of all particles in a system, you can derive all past and future paths of the particles. It doesn't seem ...
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2answers
158 views

How to reconstruct the dependence of the potential from a coordinate?

An ion moves along the x-axis of a black box with a speed $V$ and returns in a time $$T=a V^b$$ where $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of a field ...
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61 views

Simulating Phase Space Evolution

I am interested in modeling the time evolution of phase-space $\rho(\vec{q},\vec{p},t)$. I have attempted to use Liouville's theorem $\partial_t\rho=-\sum_{i=1}^{3}(\partial_{q_i}\rho)\dot q_i+(\...
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170 views

Is there an error in Susskinds' derivation of Euler-Lagrange equations?

http://imgur.com/kZO5C0V First, I believe there is a trivial error. The second equation should have another $\Delta t$ multiplying everything on the right. It is divided out later when the equation ...
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2k views

How to calculate when an object will fall over

TL;DR Given the point of centre of mass, width of base and height, is there a way to calculate the angle where the object will fall over? The TL;DR of this question pretty much sums it up, however I ...
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58 views

Sum of velocity fields

In hydrodynamics the for a non-viscous flow the velocity (and density) fields are given by the continuity and Euler equations: $$\rho\frac{\partial \vec{v}}{\partial t}+\rho(\vec{v}\cdot\vec{\nabla})\...
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Derivation of ensemble distribution

I heard that you can derive the canonical ensemble by maximizing $L = \sum_i p_ilog( p_i ) + \alpha (\sum_i p_iE_i-E)$ or for the grand-canonical ensemble $L = \sum_i p_ilog( p_i ) + \alpha (\...
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122 views

What is difference between anisotropy and inhomogeinity of this type of composite material?

I am studying some types of composite materials having 2 phases - fibers and matrix. I have some questions and confusions. Any help is appreciated. The composite has fiber along length and I am ...
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121 views

Rotational Mechanics: Conservation of Angular Momentum

Consider a case where a person stands on top of a rotating disk. The disc is given to rotate at a constant rate. There are two possible movements of the man: He moves away from the center: In this ...
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129 views

De Donder Weyl theory

Im trying to get my head around what the difference is between a symplectic and multisymplectic manifold is. My understanding currently is that on a symplectic manifold time is the parameter that "...
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3answers
118 views

Why do we add the spin angular velocity and orbital anglar velocity when asked to calculate total angular velocity of Gyroscope?

Normally when we talk of angular velocity we mean how the angle of a vector changes with time with respect to an origin.Thus the oribital angular velocity of gyroscope makes sense to me.However I find ...
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288 views

Confusion in Euler-Bernoulli beam theory

Euler-Bernoulli beam equation is given by $$ EI \frac{\mathrm d^2 u}{\mathrm d x^2} = M'(x) \\ EI \frac{\mathrm d u}{\mathrm d x} = xM'(x) + C_1 $$ Where, $E$ is modulus, $I$ is second moment of area,...
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169 views

Can the angular momentum of any rigid body (symmetrical or asymmetrical) be found this way?

Can the angular momentum of anybody regardless of whether its symmetrical about the center of mass or not be found by finding the angular momentum about its center of mass and summing it up with the ...
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354 views

Power dissipation in High Voltage Cables

I was doing the following physics problem in physics class: You have two dimensionally identical pieces of metal, one made from aluminium the other made from iron. It is given to us that ...
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821 views

Steering a motorcycle

From my experience riding, at low speeds (between 0 and 10 mph) you mostly steer the bike with the handlebars. What I mean by this is if you want to turn left you rotate the handlebars ...
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268 views

Conservative force as a potencial energy gradient

A conservative force $\vec{F}$ is apparently defined as the gradient of a potential energy $U$: $$\vec{F} = -\nabla\ U$$ I am curious if this definition was originally used to describe a ...
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141 views

How to reconcile these two approximations?

I'm working on what should be a simple problem (Taylor Classical Mechanics problem 6.23.), but I'm having a tough time reconciling the many ways it can be tackled. An aircraft whose speed is $v_0$ ...
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137 views

Integrals of Motion for s Degrees of Freedom

From Landau & Lifshitz, Classical Mechanics, the number of integrals of independent integrals of motion for a system of $s$ degrees of freedom is $2s-1$. I am considering a spherical pendulum in ...
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2k views

Difference between Hamiltonian in classical Mechanics and in quantum Mechanics

I have a question about difference between Hamiltonian function (the description of system in classical physics) and the Hamiltonian operator (quantum mechanics). I think that there two different ...
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391 views

Water bottle moment of inertia

I've noticed that I can make a full water bottle spin about its short axis easier than I can make it spin when it is 1/4 or 1/2 full. Also, when it is spun and is not full, the geometric center of the ...
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189 views

Work done against a resistive force

My past year exam paper had a question about work done against the resistive force, where the answer key said it was resistive force * distance. As I understand it, work done is a measure of impact a ...
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Since everything with mass exerts a gravity force on everything else, why do objects float in outer space?

For example, if you were to go out into deep space, and just slow down and stop your rocket. Everything inside the rocket that's not strapped in, starts floating. Why is that if every object has mass ...