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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Summation notation for Kronecker delta

I'm having some problems on notation for indices: I've found in Goldstein, 3rd edition, that the Kronecker delta satisfies the following property: $$\delta_{ij}\delta_{ik}=\delta_{jk}$$ But ...
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107 views

What are possible explanations for the permeability of balloon rubber, PET plastic and other synthetic materials for carbon dioxide?

Balloons are definitely not gas-tight. Carbon dioxide just leak by the rubber away. A balloon is filled with carbon dioxide. Knot in it. And play. Shrinkage. After an hour or two the carbon dioxide ...
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88 views

Fluid mechanics -Question about boundary?

Problem statement: A two-dimensional fluid stream of thickness $S$ and velocity $c$ (evenly distributed through the thickness of the stream) falls on a stationary plate and gets separated. Calculate ...
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2answers
324 views

Turning points of particle

A particle of mass $m$ and energy $E<0$ moves in a one-dimensional Morse potential: $$V(x)=V_0(e^{-2ax}-2e^{-ax}),\qquad V_0,a>0,\qquad E>-V_0.$$ Determine the ...
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38 views

How did we get rid of the term $\overrightarrow{G}_W$? [closed]

Equation of conservation of momentum: $$\frac{d}{dt}\int_{W}\rho \overrightarrow{u}dV+\int_{\partial{W}}\rho \overrightarrow{u} (\overrightarrow{u} \cdot ...
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1answer
75 views

Using tensors on Lagrangian and Hamiltonian

We can write the Lagrangian (with $n$ generalized coordinates) using the following expression: ...
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0answers
77 views

Area Integrals when Calculating Force Exerted by Air Pressure [closed]

I'm trying to find the force exerted on the walls of a cavity being filled with air. This involves doing area integrals, which I'm struggling with. The setup below is slightly complicated, see the end ...
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1answer
105 views

Trivial conserved Noether's current with second derivatives

I'm considering a symmetry transformation on a Lagrangian $$ \delta A = \int L(q +\delta q, \dot{q} + \delta \dot{q} , \ddot{q} + \delta \ddot{q}) dt $$ the general variation takes the form $$ ...
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1answer
69 views

How does the Hamiltonian change when going to a moving frame?

The Hamiltonian of a free particle in a rotating frame is given by $$ H = H_0 - \omega \cdot J, $$ where $H_0$ is the Hamiltonian in the non-rotating frame, $\omega$ is the angular velocity of the ...
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1answer
249 views

Symplectic leaves, tori and Poisson manifolds

For classical systems we can define a configuration manifold, whose cotangent bundle is a momentum phase space equipped with a closed, non-degenerate 2-form. Upon the commutative algebra of smooth ...
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2answers
65 views

Proof that oscillations in 1d potential well occur between certain points

In >>this<< situation, a particle with energy $E$ will oscillate between the positions $x_1$ and $x_2$ indicated on the diagram. This simple fact is taught in many introductory courses however I ...
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37 views

When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)? [duplicate]

When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)?
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28 views

What physical parameters are really being described when a rope manufacturer cites “elongation %”?

I have a precision pulley system sensitive to micron displacements. I am having issues because I need a cord with low tensioning force, but also low stretch. I am getting some weird hysteresis in the ...
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1answer
28 views

Motion in oscillating field: expanding in powers of $\xi$ [closed]

I'm reading an excerpt from Landau/Lifschitz's Mechanics book about motion in oscillating fields. Two equations for the motion of a particle with mass $m$ are set out: \begin{equation} m\ddot{x} = ...
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2answers
67 views

How 'rare' is no-slipping?

I have come across a lot of questions that say something like: A ball rolls down a hill without slipping... But I have done the maths and found that a ball would only 'not slip' if the friction ...
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2answers
121 views

Angular momentum and the Units

I'm just curious about why many physical identities build relationship with the same units as angular momentum like the action, Lagrangian$\cdot$time, Hamiltonian$\cdot$time, phase space area etc?
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1answer
113 views

simple question on torques on an ellipsoid

I have an ellipsoid, and in the reference frame where the x-, y- and z-axis are aligned with its eigenvectors I compute the torque $\vec\tau$ acting on it. And I'm asking myself how can I quantify ...
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1answer
123 views

Work and chemical energy “paradox”

This is a mistake I've seen many people make, a few physicists included, but I haven't ever seen a satisfactory explanation for what's going on. Apologies for the lengthy setup. Setup Suppose I ...
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6answers
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Why is a beam reach the fastest point of sail on modern sailboats?

I've heard that a beam reach (perpendicular to the wind) is the fastest point of sail on modern sailboats, but I haven't heard a satisfying explanation of the physics behind the claim. Triangular ...
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1answer
56 views

What does a scale accelerating on an incline read?

I was watching an online video lecture about dynamics, and then I came across this brain teaser, and I've been thinking it over for a couple of hours but can't seem to find the solution. I hope ...
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4answers
380 views

How to prove that any rotation can be represented by 3 Euler angles

How can one prove that any rotation of a rigid object in 3-dimensional (3D) space can be represented by a sequence of three rotations around pre-fixed axes by 3 Euler angles? I see this statement in ...
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0answers
51 views

Force acting on a wheel of a two-wheeled self balancing bot

Proceeding further with my work on a self-balancing bot as posted here: http://bit.ly/1FfI6LK I've gotten stuck at the following equation: n = Gear ratio $K_t$ = DC motor torque constant $i_l$ = DC ...
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1answer
123 views

Angular acceleration as a function of torque

I know that the angular momentum $\mathbf{L}_{cm}$ with respect to the centre of mass of a rigid body can be expressed as $I\boldsymbol{\omega}$ where $I$ is the inertia matrix and ...
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1answer
85 views

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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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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1answer
127 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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1answer
321 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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1answer
82 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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56 views

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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1answer
27 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
82 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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1answer
79 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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1answer
93 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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2answers
549 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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15 views

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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1answer
115 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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36 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
1k 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
2k 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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1answer
197 views

Components of acceleration in spherical polar co-ordinate [closed]

I wanted to calculate two component of acceleration in polar co-ordinate. Starting from the lagrangian $$L= \frac{1}{2}m( \dot{r} ^{2}+ r^{2} \dot{ \theta } ^{2} ) -V(r, \theta )$$ I ...
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4answers
281 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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1answer
87 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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2answers
98 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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1answer
96 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 = ...
2
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1answer
47 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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1answer
229 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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73 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
110 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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1answer
271 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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1answer
131 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 ...