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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Reach every point in phase space

I want to find out whether a 1d-system with the potential $$V(x):=V_0 (1- |x|)^2$$ meets every point in phase space for $x \in [-1,1]$(or comes arbitrarily close to it), which would mean that my ...
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56 views

Why isn't jumping against a wall an elastic collision?

According to this calculator http://www.abecedarical.com/javascript/script_collision1d.html when low mass object hits high mass object it is reflected gaining opposite velocity almost the same as ...
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49 views

If you dig a deep tunnel, will the rock sublimate?

If a tunnel is dug deep inside the crust (but before reaching places where the rock is liquid), how will the enormous downwards pressure manifest itself? Will the difference in pressure ...
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22 views

Energy and momentum as partial derivatives of on-shell action in field theory

According to L&L, if we fix the initial position of a particle at a given time and consider the on-shell action as a function of the final coordinates and time, $S(q_1, \ldots, q_n, t)$, then... ...
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46 views

Which way to lean when driving a gokart?

Given a car that has two lines of wheels, the center of gravity at constant height above the ground, constant turn angle and given surface and wheel material. What is the maximum speed the car can ...
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64 views

Force Diagram for K&K 2.13 [on hold]

I have been (independently) working on Problem 2.13 in Kleppner and Kolenkow's An Introduction to Mechanics and come to an answer which conflicts with the hint the authors provided in the book. The ...
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73 views

What is the “associated scalar equation” of equations of motion?

In an essay I am reading on celestial mechanics the equations of motion for a 2 body problem is given as: $$\mathbf{r}''=\nabla(\frac{\mu}{r})=-\frac{\mu \mathbf{r}}{r^3}$$ Fine. Then it says the ...
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34 views

What does an $n$-body system with constant $T$ and $U$ look like?

Can someone give an example of a system where the kinetic $T$ and potential $U$ energy are constant (but not zero)? Here's what I have in mind: Say you have $n-1$ satellites of negligible mass ...
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20 views

Degrees of Freedom for an Asymmetric top

How many degrees of freedom does an asymmetric top have if it is rotating about a fixed point?What are the generalised coordinates used then?
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205 views

Why is this the volume flow rate per unit area?

In fluid mechanics we consider a fluid filling a region $D\subset \mathbb{R}^3$ together with a function $\rho : D \times \mathbb{R} \to \mathbb{R}$ called the mass density such that for any ...
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36 views

Intuition behind the principle of virtual work

To derive Lagrange's Equations we need the principle of virtual work first. This principle states that whenever a system of $K$ particles is constrained to a submanifold $\mathcal{M}\subset ...
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37 views

Liquid Column “Recoils” in a Sealed Cylinder When Hit by a Piston — Is it Possible?

Consider a cylinder filled partially with a liquid (e.g. water). The cylinder is sealed, and is at held at room temperature (e.g 298K). At equilibrium (or when no external disturbance is imparted to ...
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29 views

Gauge formalism in rigid body mechanics

When doing calculations in rigid body mechanics, it is necessary to choose an origin to calculate torques and angular momenta. However, the underlying dynamics does not depend upon the choice of that ...
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35 views

How to prove that generalized coordinates are independent?

I know that the generalized coordinates obtained after taking into account the constraint forces are independent. How can I prove this?
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45 views

How can I derive the Hamiltonian of simple harmonic oscillator from this Lagrangian?

I'm working through Leonard Susskind's Theoretical Minimum: Classical Mechanics and I can't seem to understand how the Hamiltonian of a simple harmonic oscillator is derived from the following ...
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22 views

Equations of motion for controlled/driven classical systems? Does D'Alembert's principle apply?

I'm puzzled about how to derive the equations of motion for certain classical systems where some entity is controlling some of the DOFs. For example, consider a double-pendulum, with lengths $l_1$ ...
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29 views

Examples of projection of angular velocity

I am looking for examples where the projection of angular velocity vector onto a different axis, has some interesting physical meaning in day-to-day contexts. For example, if a gramophone turntable ...
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39 views

Does lever needs gravitation to work? [closed]

Simple question - Does lever needs gravitation force to work or it just needs fulcrum and could work in vacuum as well?
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73 views

Force applied to an inclined plane

Below is a picture of the problem. Any guidance would be helpful. This problem isn't actually from any assignment, per se. I'm hoping that, by understanding this, it'll help me to understand a ...
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38 views

How can one diagonalize the second variation of action?

Suppose we have action $S[q]$ and its stationary path $q_s$, I want to find the orthonormal paths $\psi_n$ that can diagonalize the second variation of the action $S[q]$. How to do that? Thanks
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80 views

What is the work done against a force?

Suppose a particle travels a path $\gamma : I\subset \mathbb{R}\to \mathbb{R}^3$ subject to a force $\mathbf{F}: \mathbb{R}^3\to T\mathbb{R}^3$, then we know that we define the work done by the force ...
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79 views

Could the center of the combined mass of the entire galaxy change if there were no external forces acting on that galaxy?

Everything in the galaxy orbits the center of the combined mass of the entire galaxy. So could the center of the combined mass of the entire galaxy change if there were no external forces acting on ...
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81 views

Configuration manifolds and constraints

In Classical Mechanics there's this notion of configuration manifold. Although I've heard about that a lot and although I often use that concept, I'm not sure I really understand them well because ...
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126 views

Story about a mathematician, a dinner party, and the three-body problem

I remember dimly hearing a story, coincidentally also at a dinner party, and I was trying recently to track the details down with no success. I was hoping someone here might have also heard this story ...
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103 views

“A Crash Course in Lagrangian Dynamics”. Is it still available online?

In an Amazon review of "Schaum's Outline of Lagrangian Dynamics" I found this: I recommend that you type "Lagrangian Dynamics" into Google and look at some of the excellent sets of lecture notes ...
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63 views

Understanding action reaction in an example

When I move an object that object should move me as well. I tried standing on a skateboard to reduce friction, and holding a heavy barbell, move myself away from it (while still holding it) but I ...
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Requesting some research study problems on Classical Mechanics [duplicate]

Someone please tell (advice) me some research study problems on Classical Mechanics that can be tackled with Undergraduate level knowledge.
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31 views

Young elasticity modulus anisotropic media

Im studying anisotropic system composed by a elastic matrix (Young modulus $E_m$) filled with oriented rods. Given this filler orientation, the material is elastic-anisotropic, with Young elastic ...
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Why does every post here gets downvoted and disregarded? [migrated]

Why does every post here gets downvoted and disregarded, even though many users here are not even professional physicists? Much condescension and feeling of self value, for someone as partial, dont ...
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How do crocodiles jump?

In a video (Here), I saw crocodiles jump vertically about three meters without using any solid surface. The wonderful thing is that when they start to jump, their vertical velocity is approximately ...
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76 views

Interesting Hamiltonian System

The definition of a Hamiltonian system I am working with is a triple $(X,\omega, H)$ where $(X,\omega)$ is a symplectic manifold and $H\in C^\infty(X)$ is the Hamiltonian function. I am wondering if ...
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179 views

A confusion about notation in Goldstein

On treating systems of particles, Goldstein starts with the consideration that whenever there are $k$ particles on a system, the $i$-th one obeys the relation $$\dfrac{d}{dt}{\bf p}_i = {\bf ...
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397 views

What exactly is a virtual displacement in classical mechanics?

I'm reading Goldstein's Classical Mechanics and he says the following: A virtual (infinitesimal) displacement of a system refers to a change in the configuration of the system as the result of any ...
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23 views

Indicate if objects after collision will stick

Is it possible to indicate if objects after collision will stick together knowing their properties(materials,hardness,etc)?
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43 views

point-particle vs rigid-body [closed]

As pointed out here point-particle-based modeling can lead to very inaccurate predictions. Could you give an example where point-particle-based model describes reality accurately enough and one where ...
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2answers
101 views

Pendulum with changing length over time. What's wrong?

I tried to find the equation of this pendulum, but I think I did something wrong. I know I have to get the Bessel's equation but I can't see it. It's a simple 2-D pendulum, without any dissipation. ...
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419 views

Classical analogue of Heisenberg and Schrödinger pictures?

What do the Heisenberg and Schrödinger pictures in quantum mechanics correspond to in classical mechanics (if they correspond to anything)? It's kind of weird, because (if I understand it well) in ...
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90 views

Link between Quantum and Classical Mechanics [duplicate]

In classical mechanics we have momentum as generator of translation by following definition: $$f(x+\delta x)=f(x)+[f(x),p]\delta x+....$$ I was wondering whether using this relation and commutation ...
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59 views

Lagrangian Systems

Given a manifold $M$, Arnold's "Mathematical Methods of Classical Mechanics" defines a Lagrangian system as a pair $(M,L)$ where $L$ is some smooth function on the tangent bundle $TM$. The function ...
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1answer
67 views

Is Gravitational Red shift equal to $mgh$

Is gravitational shift - $\frac{gh}{c^2}$ (according to pound-rebka experiment) always equal to $PE=mgh$? because assume the gravitational pull, $g$, is equal to $1$ then we can say $g = 1$ similarly ...
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139 views

Naive questions on the concept of effective Lagrangian and equations of motion?

Let us consider a LC circuit containing an electric dipole moment, the quantum system (electric field $E$ coupled with a dipole moment) can be described by the path integral $$Z=\int DEDxe^{i\int ...
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22 views

Canonical transformation that contains the time as an explicit parameter

On the Page 385 of Goldstein's Classical Mechanics book (third edition), it starts to talk a bout the canonical transformation with time as an explicit parameter. But I don't quite under understand ...
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33 views

hydraulic scissor jack lifting capacity

Can you please assist with a really simple question? I have a hydraulic scissor jack table with the following: 2 hydraulic cylinders, each with a cylinder stroke of 240mm, a cylinder bore of 50mm ...
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1answer
43 views

Interaction of solid objects and change of trajectory

I have two solid objects. Each of them has an arbitary complex surface, which is discribed by set of vertices. The aim is to describe their interaction, result of which is the change in trajectory of ...
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71 views

Macroscopic Forces from QED

In QED the carrier for electromagnetic interaction is a photon, while macroscopic forces are due to electromagnetic interaction (by macroscopic forces I mean: normal force, object collision, friction ...
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88 views

Cartesian Coordinates to Polar Coordinates

I apologize if this question is trivial, but I am new to physics and am struggling with some of the basic concepts. Working in $\mathbb{R}^2$ with standard coordinates $(x,y)$, suppose we have a ...
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68 views

What could cause an asymmetric orbit in a symmetric potential?

My question can be summarized as: Given a potential with a symmetry (e.g. $z\rightarrow-z$), should I expect orbits in that potential to exhibit the same symmetry? Below is the full motivation for ...
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1answer
44 views

What indicates if object will be reflected - certain example

If I throw a small rock(1kg) at a big rock(100kg) the small rock is reflected; Let's say my weight is 80kg - if I would jump into a big rock instead of being reflected I would move in the same ...
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71 views

Where does energy go when performing a useless effort?

I went to school one day, so I thought I was able to get this simple one.. but it looks like I'm not anymore. :( One lonely little spaceship is resting into space. It has a small fuel capacity that ...
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How do I calculate motor efficiency from voltage, current and RPM?

I have a setup where a motor is spinning at a constant (known) RPM, under no load. I know the power going into the motor (voltage * current), and I can find out the rotational kinetic energy of the ...