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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Can someone explain what's the difference between all these terms in “Simple Words” with their “applications”? [closed]

I'm very confused between all these terms. Can someone explain what's the difference between Classical Mechanics, Relativistic Mechanics, Quantum Mechanics, Quantum Field Theory, ...
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288 views

What is the difference between configuration space and phase space?

What is the difference between configuration space and phase space? In particular, I notices that Lagrangians are defined over configuration space and Hamiltonians over phase space. Liouville's ...
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111 views

How does one express a Lagrangian and Action in the language of forms?

In Lipschitzs Classical Mechanics a Lagrangian is defined as: $L(q,q',t)$ for some trajectory $q(t)$ of a particle And the action is defined as: $S:=\int^a_b L(q,q',t) dt$ How does one ...
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120 views

Solving the Three-body problem numerically

I want to create a program in $Mathematica$ that solves numerically the Three-body problem by Euler-Lagrange's equations. I was searching some methods to sucessfully do it. So I found a way to solve ...
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62 views

Hamilton-Jacobi problem

In analytical mechanics by Fasano and Marmi they consider the Hamilton-Jacobi equation for a conservative autonomous system in one dimension with the following Hamiltonian, \begin{equation} ...
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Conservation Laws and time-reversal symmetry [duplicate]

In most dynamics books I've read they refer to conservation laws and their associated symmetries, cf. Noether's theorem. I know that the conservation of momentum is a result of the homogenity of ...
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25 views

What can I say about a graph depicting orbit a particle has gone through? Acceleration VS friction

I have an orbit in which a particle is told to have gone through. There is a straight part, and a curved part. I am asked to mark the right statements, which are: a. Without any further data, there ...
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1answer
37 views

Degrees of freedom of a point mass sliding on a rigid curved wire without friction

I am very new to the subject and am going through Structure and Interpretation of Classical Mechanics. One exercise asks to find the degrees of freedom of a number of systems, one of which is a ...
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100 views

Jacobi energy function $h$ and the Hamilton $H$ and the Hamilton-Jacobi equation

My understanding of the Jacobi energy function $h$ as defined in Goldstein is that it is the total energy $T+V$ expressed as, \begin{equation} h(q,\dot q,t)=\sum \frac{\partial L}{\partial \dot q}\dot ...
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63 views

Proving independence of the lagrangian on position of a free particle using the euler-lagrange equation

I asked a similar question some time back but am trying to work this from another angle. In deriving the lagrangian of a free particle, we use the homogeneity of space to conclude that the lagrangian ...
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58 views

Maximum range of projectile from elevation, simply?

Let us say you have project a ball at velocity $u$ from a cliff hight $h$, and we want to find the maximum range of the ball. Ok so you could do this using equations of motion (for constant ...
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133 views

In which direction does mud fly off a moving bike's tire & why?

If a bike moves through a muddy area, mud gets on its tires. Then the mud flies off from the tires. Which forces are acting on it? In which direction does it fly off? On my physics test, I wrote ...
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How this tube rotates? [duplicate]

I recently seen a video where a tube is spin into space. When it starts to rotate, it keeps continuously to rotate along the axis of 180 degrees clockwise, then 180 counter-clockwise and so on. The ...
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82 views

Lagrangian for free particle in special relativity

From definition of Lagrangian: $L = T - U$. As I understand for free particle ($U = 0$) one should write $L = T$. In special relativity we want Lorentz-invariant action thus we define free-particle ...
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33 views

name of this bouncing balls separator model

https://www.youtube.com/watch?v=SRGf0Mq2Zwg I want to read the physical and mathematical model of this "bouncing balls separator " in the above link . What is name of this experiment so I can search ...
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2answers
145 views

Relation between magnetic moment and angular momentum — classic theory

How do I prove the relation between the vectors of magnetic moment $\vec\mu$ and angular momentum $\vec L$, $$\vec\mu=\gamma\vec L$$ ? Many text books and lecture notes about the principles of ...
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3answers
343 views

Is there a quick way of finding the kinetic energy on spherical coordinates?

Assume a particle in 3D euclidean space. Its kinetic energy: $$ T = \frac{1}{2}m\left(\dot x^2 + \dot y^2 + \dot z^2\right) $$ I need to change to spherical coordinates and find its kinetic energy: ...
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4answers
144 views

Classical and quantum systems [closed]

What are the main differences between a quantum and classical system? How does one can distinguish them?
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58 views

Deriving lagrangian of a free particle - How do you arrive at Lagrangian independency conclusions

I guess this question has been asked before, but I'm looking at a slightly different aspect. I'm reading Landau's book on classical mechanics. In deriving the lagrangian for a free particle, I ...
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78 views

do the planes of electron orbits make an angle?

if we think as the electrons around the atoms classically, then as the two electrons in the first shell (1s) go around the nucleus; do the planes of orbit make an angle with each other (as an average) ...
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78 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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1answer
38 views

What stops the middle point of a power line from falling?

Say you have a system that is a uniformly weighted string with slack suspended from two points; i.e. a power line. There are three forces acting on any given point on this string: string tension ...
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224 views

Why do some impact craters have an elevation in the center?

Why do some impact craters have an elevation in the center? What processes lead to its formation?
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61 views

Decoupling of generalized coordinates in lagrangian

Say you have a lagrangian $L$ for a system of 2 degrees of freedom. The action, S is: $S[y,z] = \int_{t_1}^{t_2} L(t,y,y',z,z')\,dt \tag{1}$ If $y$ and $z$ are associated with two parts of the ...
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1answer
71 views

Is there a speed limit for objects falling in gases or liquids? [duplicate]

Let $o$ be a spherical object with mass $m$ and surface $s$. Let $g$ be the gravitational acceleration and $h$ the height. Let the gas where we drop $o$ in have density $d$ and pressure $p$ at ...
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199 views

Is there a rotational equivalent to newtons laws?

Newtons three laws of motion appears to apply only for linear motion: An object remains at rest or moves in a straight line at uniform velocity unless a force is applied. Force is mass times ...
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96 views

Is it true that the self-force prevents a classical particle from falling into a Coulomb potential? What is the physical explanation of this result? [closed]

In 1943 CJ Eliezer published a paper claiming that the self-force prevents a zero angular momentum particle from ever reaching the center of an attractive Coulomb potential (and what's more that it ...
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30 views

Ratio of oscillation amplitudes of a box on a gasket to floor

So the problem is that I have a box and I put it on a gasket to preserve it from vertical oscillations. The gasket is compressed by the box by a quantity of $h$. The floor is oscillating at frequency ...
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1answer
76 views

Can you determine acceleration from positions and velocities only?

I just began reading the Landau and Lifshitz book on classical mechanics. It states on the first page of Chapter 1 that: Mathematically, this means that, if all the coordinates $q$ and velocities ...
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1answer
66 views

Cart speed and wheel rotation

Say you have a horse drawn cart. Does the outside of the wheel spin at the same velocity that the cart moves forward? The reason I ask is because I am working on a problem where a piece of mud ...
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0answers
46 views

Hamiltonian flow?

I was wondering what the Hamiltonian flow actually is? Here is my idea, I just wanted to know if I am correct about this. So let $(x(t),p(t))' = X_{H}(x(t),p(t))$ are the Hamilton's equations and ...
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1answer
119 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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105 views

Lagrangian $L' = L + \frac{df}{dt}$ gives the same equations of motion

It is well known that when a Lagrangian $L$ is incremented by the total time derivative of a function $f$ that does not depend on the time derivatives of the generalized coordinates, the same ...
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Can dimension analysis be used in developing more advanced physics equations?

It is obvious that dimensional analysis can be used to derive many classical mechanics equations (excluding constants). As long as all the dependent quantities are known. My question is whether this ...
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1answer
41 views

How to find the spring coefficient of a simply supported beam?

So I've been searching wikipedia and google but nothing can show how to find the spring coefficient of a simply supported beam with a uniformly distributed load. The spring coefficient, $k$, is ...
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2answers
174 views

Can the coefficient of friction be derived from fundamentals?

It is common to want to derive macroscopic laws from what we know microscopically - after all, given a (correct) microscopic description, everything larger should follow. Has it ever been done to ...
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22 views

Does the force of releasing the latch of a spring-latch contraption affects the force generated by the spring?

There is this contraption in my class, where a rod is attached to a latch and a spring. By pulling the latch back behind a piece of metal, the latch is secured, the rod if pulled back and the spring ...
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1answer
81 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 ...
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1answer
71 views

Orbital angular momentum of electrons

In a QM class, to study the hydrogen atom, we started by defining the Hamiltonian $H$ for a central potential, then made an orbital angular momentum operator appear as part of $H$, then down the line ...
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1answer
20 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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35 views

$\mathbf{P}=M\mathbf{v}_{cm}$ for a continuous body?

While restudying some fundamental concepts with greater attention, I have reflected on the following deduction, which I find in my book of mechanics, of the identity of the temporal derivative ...
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Usage of concept of static deflection on classical mechanics (ex. SHM based problems)

Can anyone explain how the concept of static deflection (static displacement) is used in problems of SHM? Explanation by/with an illustration would be even the more helpful. Thank you
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2answers
61 views

Spring on a rotating disc [closed]

An object (with mass m) is attached with two identic springs (with spring constant k) to the edge and the axis of a rotating disc (with radius r). The object undergoes no friction and is in the middle ...
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49 views

Total angular momentum of a continuous body

I find the definition of total angular momentum $\mathbf{L}$ of a system of $n$ material points with respect to a given point $Q$ as the sum of the momenta $\ell_i=\mathbf{r}_i\times\mathbf{p}_i$ ...
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2answers
76 views

Amplitude-phase decomposition as a canonical transformation

I am studying a classical dynamical system defined on $\mathbb{CP}^2$: the phase space is parametrized in terms of three complex coordinates $\psi_i$ ($i=1,2,3$) and Hamilton's equations of motion ...
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1answer
122 views

What is the idea behind canonical quantization?

From what I understand, canonical quantization of a classical theory consists of replacing the observables by abstract operators, of which only the commutation rules, which have to correspond to the ...
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33 views

Acceleration of an oscillating object in a frame of reference that is itself rotating!

I have been reading a paper and due to my limited knowledge of Physics, I can't move ahead. Sorry I do not know latex so, I will snip the paper and paste it here. So here goes it..... I think ...
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30 views

Physical interpretation of the relative displacement tensor?

I've resolved a relative displacement tensor into a strain tensor and a rotation tensor, where the strain tensor is: $$ \varepsilon_{i,j} =\begin{pmatrix} 0.2 & 0 & 0 \\ 0 & 0.8 ...
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How does electromagnetic radiation affect the velocity of a charged particle?

I've heard that the acceleration of a charged particle releases electromagnetic waves. So let's say there is a charged electron moving forwards in a region with a downwards magnetic field. If the ...