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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heap of pebbles

It is common to see a heap of conical shape formed by a large number of similar size hard spherical objects, for example, a heap of pebbles, sand etc. Suppose we want to model this system as a ...
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How does constant thrust avoid quadratic kinetic energy accumulation?

I haven't found the right search terms for this question, so if it has been answered, references would be welcome. Suppose we start from experimental station in deep space (interstellar space if need ...
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Coordinates from action-angle variables

I'm interested into getting the original coordinates, $q(t)$ and $p(t)$, from the action, $J=\oint p dq$, and angle, $w(t)=\frac{dH}{dJ}t+\beta$, variables for a 1-D, one particle system. I know that ...
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42 views

Confused about something in Landau classical mechanics

On page 7 in Landau and Lifshitz Mechanics He writes: We have $L'=L(v'^2)=L(v^2+2ve+e^2)$ now the confusing part comes (for me): He writes: Expanding this expression in powers of e and neglecting ...
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52 views

Lagrangian Mechanics + Account for friction of block

$\newcommand{\dd}{\mathrm{d}}$ I am trying to work out the Lagrangian mechanics for a pendulum problem in order to animate it. I'm working on one of the examples in the Wikipedia page on Lagrangian ...
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12 views

Ultrasound Transducers and Simulator [closed]

Presently I am working on Underwater Acoustic Wireless Transmission. I desire to measure water parameters at the bottom of the surface of the water and then pass it to the water surface using ...
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1answer
141 views

“Principle of least action” and “Principle of conservation of energy”: Which one is fundamental and which one is derived? [closed]

Suppose I throw a ball upwards. First it will rise under gravity and then fall under gravity. During the rising part the kinetic energy gradually decreases and the potential energy increases until ...
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1answer
92 views

Does Dirac's argument against classical mechanics stand in contradiction to Bohm's theory?

In his book on Quantum Mechanics, P.A.M. Dirac talks about the stability of the atom as a means of demonstrating the need for quantum mechanics. He writes: The necessity for a departure from ...
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34 views

Pendulum in radial gravity field

All I could find about pendulums assumes that the force on the pendulum mass m is mg directed downwards. The case of m being attracted only by the radial gravity pull (thus replacing the "plane" ...
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0answers
68 views

Are there any conditions under which the Christoffel symbols can be treated as a damping term in a harmonic oscillator?

(Mathjax did not seem to be working as I composed this question. Hopefully it will kick into action once I post.) Note I am a novice at tensor notation. I am working with the following Lagrangian ...
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0answers
44 views

Lyapunov stability of circular orbits

I'm studying Classical mechanics on Arnold's "Mathematical Methods of Classical Mechanics". In a problem i'm asked to find for which $\alpha$ the circular orbits in the central field problem are ...
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0answers
30 views

Are these torques correct for a simple balancing/fulcrum experiment?

For my physics lab, they had us do a simple static equilibrium experiment where we rested a ruler on a fulcrum (at its center of mass) and then attached varying amounts of weight on either end at ...
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33 views

Calculating car engine RPM from inputs [closed]

So I am willing to calculate engine RPM of car. The usual process for doing this in games is: $\omega_\mathrm{e} = \omega_\mathrm{w} * D_\mathrm{k} * g_\mathrm{k} * 60 / 2\pi$ However, this ...
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2answers
637 views

Thermal energy generated due to loss in kinetic energy when observed from two different frames of reference

A body is moving with a velocity $v$ with respect to a frame of reference $S_1$. It bumps into a very heavy object and comes to rest instantaneously, its kinetic energy $$\frac{1}{2}mv^2$$ as ...
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1answer
49 views

Statistical Mechanics problem regarding the enthalpy and the expected value of energy

So I have an assignment(relating to a chapter on Canonical Ensemble) here with $H_E = \langle H\rangle$ where $H_E$ is the enthalpy, and $\langle H\rangle$ is the average of the Hamiltonian, I think. ...
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0answers
19 views

Max & inflection point in the principle of least action [duplicate]

Short question: What is the physics interpretation of max & inflection points in the principle of least action? Long question: If $$L(q_1,q_2;t)=K-V$$ then let $$S = \int^{t_1}_{t_2} ...
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0answers
28 views

What are the implications of phase transition on electromagnetic device? [closed]

for the analysis of ferromagnetic materials on which I confirmed existence of Phase transition using Monte Carlo simulation implemented on Mat lab. contribution to knowledge are required.
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1answer
281 views

Flipping a deck of cards: why do the cards cluster?

First let me describe what I mean by flipping a deck of cards. Fan a deck out, take the card on one side, flip it - then, much like a string of dominos, the rest of the cards are flipped and end up ...
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212 views

Equation of a flying kite

My question is the following: What is the shape of the rope which holds a kite flying? (Steady state.) I am not a physicist (I am a mathematician), so I can not work the physics part of the ...
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1answer
77 views

Harmonic oscillator: if $E=\frac{1}{2} q \dot{\theta}^2+\frac{1}{2} s \theta^2$ then $\omega=\sqrt{\frac{s}{q}}$?

Consider an harmonic oscillator. Suppose that I manage to write the mechanical energy as a function of a quantity, like the angle $\theta$ in this way $$E=\frac{1}{2} q \dot{\theta}^2+\frac{1}{2} s ...
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46 views

Rolling Resistance Coefficient

I found that rolling resistance can be expressed with this equation: $$F_\mathrm{rr} = \frac{C_\mathrm{rr} W}{r}$$ Where $C_\mathrm{rr} =$ coefficient of rolling resistance $W =$ normalforce $r ...
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3answers
711 views

Why Liouville's theorem is obvious?

In Florian Scheck's Mechanics, he stated the local form of Liouville's theorem as follows: Let $\Phi_{t,s}(x)$ be the flow of the differential equation $$-J\frac{d}{dt}x=H_{x}.$$ Then for all $x,t,s$ ...
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24 views

Moving a Car the quickest path

I have a car, that has a current angle and location, and a destination angle and location. The car has a maximum linear and angular acceleration. Assume the car will always travel in the direction it ...
3
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1answer
81 views

What is the probability of two bullets to get clashed? [closed]

I was surfing on Instagram, and I found this amazing proto whose description is "the probability of such an event to happen is incredibly small, so this is a really curious finding". Well.. I'm ...
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3answers
62 views

How simultaneous information of coordinates and velocities sufficient to completely determine the subsequent motion of a mechanical system?

I somehow could not find the answers to the question in Why are coordinates and velocities sufficient to completely determine the state and determine the subsequent motion of a mechanical system? to ...
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4answers
450 views

Would a phone move upon vibration in a completely uniform situation?

I was sitting down yesterday and saw my phone vibrate on a side, and it moved about a centimetre per vibration. I wondered why it moves, and thought perhaps that the side it was on had a slight ...
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1answer
32 views

Initial velocity and time of motion through water

What initial velocity has to have a ball at the height $h=1\ \text{m}$ in order to sink in the water to depth of $s=4\ \text{m}$? How long is the motion of a ball through water? A ball is made of ...
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1answer
44 views

Force as a Function of Position

If given a velocity as a function of position, is force as a function of position just it's derivative times the mass? I'm given the following and I am not sure my above logic is correct: The speed ...
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2answers
122 views

How is the Poisson bracket $\{\mathbf{c},\mathbf{l}\cdot\hat{n}\}=(\hat{n}\times \mathbf{c})$, for constant $\mathbf{c}$, and not zero?

The Poissonian formulation of mechanics tells us that for a generating function $g(q,p,t)$, the Poisson bracket of some function/variable $f(q,p,t)$ with the generating function corresponds with an ...
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1answer
507 views

Is Wikipedia's definition of angular velocity incorrect?

According to Wikipedia, the general formula for the angular velocity of a particle in three dimensions is $$\boldsymbol \omega = \frac{\mathbf r \times \mathbf v}{\left |\mathbf r\right|^2}.$$ But if ...
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1answer
132 views

Rigorous definition of degrees of freedom

According to this Wikipedia article, the definition of degrees of freedom is: The degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its ...
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16 views

Equality of external derivatives in Canonical Transformation implies invariance of Poisson Brackets

For a canonical transformation, we require that the forms $$p'dq'- H'dt$$ and $$pdq -Hdt$$ differ up to a total differential. From this follows the equality of the external derivatives: $$\sum_i ...
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2answers
97 views

Proof that 1d lattice displacement by phonons is given $u_{n\pm 1}(t) = A_ke^{i\omega_k t} e^{i knd}e^{\pm i k d}$

I looked in «Kittel - Introduction to solid state physics», Wikipedia and Google for the derivation that: A phonon of wavenumber $k$ displaces the $s$-th atom in a monoatomic 1d crystal lattice by a ...
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2answers
76 views

Why is a sphere easier to move than a box of the same mass?

Is it only because of the less friction involved or at there other reasons?
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1answer
53 views

Rigid body motion degrees of freedom

A rigid body moving in $\mathbb{R^2}$ has 3 degrees of freedom and in $\mathbb{R^3}$ has 6 degrees of freedom. Could you please help me show that a rigid body moving in $\mathbb{R^n}$ has ...
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2answers
123 views

Work and forces in systems of many particles

I'm reading Goldstein's Classical Mechanics, first chapter, and am confused about what's going on in equations of forces and work in systems of particles. For example, Goldstein calculates work done ...
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3answers
76 views

Magnitude of Normal Force in Circular Motion

In the above diagram an object is in vertical circular motion. At $T_0$ the object is at pos1, and at that position, I have shown the forces resolved. So $F_n-mg\cos(a)$ is the centripetal force ...
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2answers
57 views

Im learning Work-energy theorem, this question popped into my mind about Force applied and displacement

I know a lot but I'm not sure, I'm guessing if $400J$ of work done on a 800 Newton object, if I'm correct, $400N$ to $800N$..that is $.5 m$ displacement, so by $W=∆KE$ why do I get $200J$? I was ...
0
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1answer
53 views

Statistical Physics of a System with Friction inside a Hot Bath

If you have a classical system (i.e obeying Newton's equations of motion) with Hamiltonian $H(x,p) = \frac{p^2}{2m} + U(x)$ then the statistical behaviour of this system is described by the ...
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2answers
44 views

How do you tell whether a force acting on an inclined plane is going up or down in its perpendicular component to the plane?

I'm practicing mechanics, and I had to resolve the following forces perpendicularly to the inclined plane in order to work out the reaction force (plus the weight of the ball) But I cannot tell ...
3
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0answers
44 views

Friction in Lagrangian Method [duplicate]

A uniform, flexible chain of length $l$, mass $m$, hangs off a frictionless table-top of height greater than $l$. The length of the part of rope hanging off is $x$. Gravity accelerates the part of the ...
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2answers
66 views

Long and short barreled guns

Projectiles containing delicate elecrtronic equipment may be damaged if they are subjected to high accelerations. For this reason, such projectiles may be fired from guns with long barrels but not ...
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0answers
21 views

Relative velocity of the center of mass in a rotating coordinate system

Say I have a rigid body in space. Let k be a stationary coordinate system, K a coordinate system rotating together with the rigid body, so the transformation $B:k \rightarrow K$ it's just a simple ...
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2answers
60 views

Can a system be designed that uses no energy to accelerate particles to high velocity?

I have one system in mind. Although I know it is not possible to accelerate a particle to a higher speed without spending energy, I would like to know why the proposed system won't work. The system ...
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1answer
40 views

Confusion with Thomas precession

Suppose an inertial frame $S^\prime$ is moving with a relative velocity $\textbf{v}=v\hat{n}$ w.r.t another intertial frame S with their axes parallel and $\hat{n}$ is an arbitrary direction. In that ...
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1answer
35 views

Why are the integrability conditions necessary and sufficient for the existence of a canonical transformation's generating function?

Consider a canonical transformation $(p,q) \rightarrow (P,Q)$ under a generating function $F$. The condition for form invariance of Hamiltonian equations of motion looks like : $$\sum_{s}P_s\dot{Q_s} ...
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1answer
28 views

A Classical/Theoretical problem regarding Friction

I had a rod. I broke it into two. Now I wish to make it one i.e. to join those (not glue or any thing as such) as if the rod was not broken at all. This is our objective! As I broke the rod apart, ...
0
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1answer
77 views

Gravitational potential energy lost by an object falling on the earth [closed]

I am stuck on this simple question: g is the strength of the gravitational field at the surface of the Earth; R is the radius of the Earth. Show an equation describing the potential energy ...
2
votes
1answer
37 views

How to scale variables in a classical Hamiltonian?

So I looked at some research articles where one has a classical Hamiltonian $H(p,q,t) = p^{2}/2 + V(q,t)$. If one introduces the scaling transformation $$t \mapsto t/\sqrt{s}, \quad H \mapsto Hs, ...
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1answer
66 views

How did he find the “lambda” value in this question? [closed]

There is a pdf i found when searching about Lagrangian Multpliers, but i was not able to understand how he derived lambda from two differential equations. If anyone can walk me through it, i would be ...