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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Bezier curve and deceleration

I have a question regarding calculation of a bezier curve. I'm programming an app where in there's continuous straight line motion of a vehicle at a constant speed. (Let's call it 'u'). When the user ...
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2answers
65 views

Converting Pendulum into Electricity? [closed]

I've been thinking about this, I want to use this as my science project. The two viable solutions I've thought of so far are magnet or rotary based. Pendulum clocks could be powered once a day and ...
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75 views

Is there any physics arguments behind NASA pen joke

I am just wondering are there any reasonable physics arguments behind difficulty making pen for no gravity conditions. My thoughts are that there are many ways to make it working as: Pressurized ...
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1answer
49 views

Q: Goldstein chapter 1 problem 16: Finding the generalized potential from the force

I have started to work through Herbert Goldstein's, Charles Poole's and John Safko's Classical mechanics, and I am having a bit of trouble with one of the problems (chapter 1 problem 16). The problem ...
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0answers
29 views

Integral of absolute value of spin angular momentum of $N$-body system

There are $N$ particles moving freely in a plane. Let $J(t)$ be the spin angular momentum of the system of particles about its center of mass. (even center of mass keeps changing with time as ...
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38 views

Normal coordinates for harmonic approximation (classical lattice vibration)

I am reading Jenő Sólyom's "Fundamentals of the Physcs of Solids" vol. 1. and i am very much stuck at this point (chapter 11.3.2 in the book): In the harmonic approximation the potential energy of a ...
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0answers
31 views

Cylinder swinging in a halfpipe [closed]

I'm having a problem while solving this exercise: Consider a cylinder of radius 'a' swinging in a halfpipe whose radius = 10a. Find the equation of motion of the cylinder using the angle $\phi$ ...
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1answer
48 views

Potential for particle rolling down slope of arbitrary shape

I've been thinking about how to calculate the potential $V(x)$ of a particle rolling under the force of gravity down some curve, given by $f(x)$ (suppose nonincreasing). My idea was to simply ...
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1answer
40 views

Minimum distance between two bodies attached by a spring

Take two bodies of masses m and M attached by a spring of constant K on a smooth horizontal surface. The system is at rest. A constant force F acts on body M, horizontally. To study the motion of the ...
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1answer
28 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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2answers
45 views

confused about the direction of friction force

I'm really confused about the direction of friction force. I think about collision of two balls and think that "friction force is opposite to the relative speed of the contact point of the two ...
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0answers
25 views

Conserved charge for boosts? [duplicate]

In (3+1) dimension Poincare group has three types of Symmetries : a) Four space-time translations b) Three spatial rotations and c) Three boosts Among them, (a) implies "conservation of ...
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24 views

calculate the tile of rotation axis of a rolling ball

I want to solve the problem of friction effect on rotation axis of a rolling ball on collision with another ball. I've read Tennis racket theorem in this wikipedia article and thought it might ...
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2answers
60 views

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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0answers
66 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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78 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
64 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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0answers
35 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
52 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
64 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
86 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
55 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
231 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
32 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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0answers
34 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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0answers
17 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
23 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
57 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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1answer
38 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
104 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
80 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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5answers
229 views

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
38 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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1answer
76 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
30 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
68 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
58 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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2answers
177 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 ...
4
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1answer
109 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
96 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
58 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} ...
4
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0answers
49 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 ...
0
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1answer
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 ...
2
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1answer
34 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
73 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 ...
2
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1answer
59 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
56 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
99 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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0answers
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
79 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 ...