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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121 views

Is the Legendre transformation a unique choice in analytical mechanics?

Consider a Lagrangian $L(q_i, \dot{q_i}, t) = T - V$, for kinetic energy $T$ and generalized potential $V$, on a set of $n$ independent generalized coordinates $\{q_i\}$. Assuming the system is ...
3
votes
1answer
113 views

Is it possible to eliminate Van der Waals interactions?

I came to know that the friction force actually depends on the surface contact area due to weak interactions (adhesion due to Van der Waals forces) between the atoms of both materials increasing in ...
2
votes
2answers
362 views

Why does a wind turbine have only three blades? [duplicate]

Why not four or five or even more? Intuitively, the more leaves the more power. So, what is the reason?
0
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2answers
65 views

Calculate small small oscillations of a pendulum

The system is setup as follows: A point $O_1$ moves along the $x$ axis with it's $x$ coordinate being $a\sin(\omega t)$ and $\omega\ne\sqrt{\frac{g}{l}}$. There's a pendulum attached to $O_1$ of ...
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0answers
23 views

Vector addition [on hold]

A pilot sets a course of 040$^{\circ}$ at an airspeed of $750$$km$$h^{-1}$. A wind blows SE at $140$$km$$h^{-1}$. Find the plane's ground speed and track. Can anyone illustrate this in a diagram?I ...
3
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2answers
83 views

Free rotation of a rigid body

So I am currently reading Fowles and Cassidy and there is something I'm confused about in the section about geometric description of free rotation of a rigid body. I will present the stuff first that ...
-4
votes
0answers
41 views

Theoretical Minimum - Lagrangian - page 124 [on hold]

It says the Lagrangian is kinetic energy minus potential energy, but he says "we can use the result from exercise 4 to get the Lagrangian" and the Lagrangian he shows only contains the kinetic energy ...
0
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1answer
85 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 ...
4
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6answers
355 views

Detecting absolute motion inside a box

This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows. ...
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2answers
136 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 ...
0
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1answer
37 views

Why is my Lyapunov exponent similar for single and double pendulum?

This is my first question here on stackexchange. I hope that I can be understood. If not, tell me and I will reformulate and fill in with details. I have simulated a single pendulum and a double ...
1
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2answers
118 views

How to reconstruct the dependence of the potential from a coordinate?

What is known is that an ion sent along the X-axis of a black box with a speed $V$ returns in a time: $$T=a V^b$$ $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of ...
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1answer
31 views

Reversing time for a closed system of particles

For a closed system of particles, the lagrangian in classical mechanics is $$L=\sum \frac{1}{2}mv_a^2 - U(\mathbf{r_1},\mathbf{r_2}, \cdots)$$ For an arbitrary position function $x(t)$, to see the ...
2
votes
1answer
93 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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0answers
24 views

Throwing the object around the Earth [on hold]

You have to throw an object to a point diametrically opposite od Earth surface, take that Earth does not rotate and that it is perfect sphere. What angle to the ground and velocity must object have? ...
2
votes
0answers
28 views

What is the optimal slope for Archimedes screw?

The Wikipedia article has nice image showing how the Archimedes screw work: As I understand, the red balls do not fall down because they are in minima caused by the screw. Because of material ...
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0answers
20 views

Local conservation law involving Hilbert Transform in a classical field theory

Consider a nonlinear PDE of the form $$A_t +iA\mathcal{H}(|A|^2_x) +N(A) =0,$$ where the Hilbert transform $\mathcal{H}$ is defined as $$\mathcal{H}(|A|^2_x) \equiv P.V. \int_{-\infty}^{\infty} ...
0
votes
1answer
31 views

Tension along a curved surface [on hold]

I'm curious what the tension in a rope will be when its exposed to a uniform load. Assuming a similar setup to this question what will the tension along the rope/tube be?
2
votes
1answer
172 views

Heuristic equation for Friction force between materials

I'm programming a game where different types of objects will be sliding over different types of terrains (Top-down in two dimensions). At my current level of physics education we are given the ...
0
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1answer
82 views

Forces Create Angular Acceleration And “Straight” Acceleration - But How Much Of Each?

Let me set up the following problem for a rectangle floating in space: We know its dimensions. We know its mass. There's a force pushing it for a known amount of time - we know the angle & ...
0
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0answers
18 views

Fun physics book for high school student [duplicate]

can anyone recommend me a physics book for a highschool student (not these typical school books) a book that will let you think mostly interested in theoretical /quantum physics done with the ...
0
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0answers
32 views

Bertrand's Theorem: Perturbative Methods Leading to $1/r^3$ Solution

My professor and I have been working on a proof of Bertrand's Theorem using perturbative methods. We have arrived at a solution yielding 1/r^3, which we had presumed to be an incorrect result. While ...
0
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0answers
23 views

Hyper/parabolic kepler orbits and “mean anomaly”

In an elliptical kepler orbit there is an easy recipe to describe the motion/position of a satellite at time $t$. One just follows the following steps - an important detail for me is that the ...
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1answer
32 views

Preventing Heat Escape

Is is possible to completely prevent heat from escaping from a closed container? Here is a diagram of vacuum flask, which tries to implement the design - Vacuum Flask prevents heat from escaping ...
1
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2answers
602 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
1
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1answer
40 views

How to determine plastic strain rate

Equivalent plastic strain rate is defined as $$ \dot{\bar{\epsilon}}=\sqrt{\frac{2}{3}\dot{\epsilon_{ij}}^{p}\dot{\epsilon_{ij}}^{p} } $$ Where, $ \dot{\bar{\epsilon}}$ is equivalent plastic strain ...
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1answer
43 views

Classical Mechanics — Sign of work done

It seems that work has two possible ways to decide it's sign: Whether you take the perspective of the system or the surrounding (whether you consider work done on the system as positive, or work done ...
0
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1answer
23 views

Comparison of the effects of collisions from an NFL Nose Tackle and a Car with roughly the same momenta

If you get hit an NFL Defensive Tackle who runs at roughly 17mph (7.6m/s) it'd hurt a lot, but if you got hit by a normal car at 1.3mph (about 0.6m/s) it hardly hurts at all, and a collision from an ...
0
votes
1answer
84 views

Explanation of force amplification inside a solenoid

For a system being actuated by a motor, the force can be amplified by gearing. The energy is being used for force instead of distance, so it produces more torque but moves slower. For a system being ...
10
votes
2answers
240 views

Are there other less famous yet accepted formalisms of Classical Mechanics?

I was lately studying about the Lagrange and Hamiltonian Mechanics. This gave me a perspective of looking at classical mechanics different from that of Newton's. I would like to know if there are ...
0
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2answers
46 views

What is the meaning of this definition of potential energy?

The isolated system of particles is being observed. In the coursebook, $\vec F_\mu$ is by definition the vector sum of forces of all other particles acting on $\mu$-th particle. Usually, potential ...
1
vote
2answers
72 views

Classical trajectories that are not a minimum of the action [duplicate]

Are there physically realizable dynamical systems where the true trajectory is not a minumum action trajectory? Formally, Lagrangian mechanics only requires that the trajectory be an extremum (or ...
0
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1answer
61 views

A course in Lagrangian Mechanics [duplicate]

I would like to know: what are some of the best introductory books to Lagrangian Mechanics?
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1answer
118 views

In a CMCS 2-body system, why does the speed of the particles after collision stay the same?

A particle $m_1$ is traveling with velocity $v$ toward a stationary particle $m_2$. The velocity of the center of mass is given as $v_c=\frac{m_1}{m_1+m_2}v$. Changing to a moving coordinate system, ...
3
votes
2answers
142 views

How do I transform onto a relativistic rotating frame of reference?

In classical mechanics, the usual formula to translate the evolution of a quantity as seen from an inertial frame of reference to a rotational frame is: $$\frac{d \textbf{A} }{dt} \vert_{Inertial} = ...
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0answers
27 views

Why does not the optical fiber break? [duplicate]

Glass is a very fragile object. So why does not the optical fiber break? Everytime I take them, I am worried about this problem.
1
vote
1answer
144 views

How is quantization related to commutation? [duplicate]

How are commutation (of observables) and quantization related? Reading about the Stone-Von Neumann Theorem, it seems that commutativity is the classical limit of quantum mechanics, and hence ...
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0answers
34 views

Time evolution of a classical system

For a harmonic oscillator the Liouville operator is given by $$L = p \partial_q- q \partial_p.$$ Now I have a phase space distribution $f(t,q,p)$ for which it holds (in general) $$f(t+\tau,q,p)= ...
0
votes
1answer
20 views

Equations of motions uneven see-saw

How do I set up equations of motions for a see-saw where the distance between the masses $m_1,m_2$ to the pivot are given by $\ell_1, \ell_2$, respectively? My idea was to first set one of the masses ...
2
votes
1answer
78 views

Optimal size of a windmill for a given windspeed

Here is the problem: Assume that you have some constant wind speed. I want to run a windmill but I need to decide how big a windmill I want. The size is characterized by the length of the blades, $r$. ...
0
votes
2answers
49 views

Proof of vertical and horizontal velocity component in projectile motion

Why is it that $v\cdot sin(x)$ gives the vertical component and $v \cdot cos(x)$ gives the horizontal component, where $v$ is the speed? What logic is there behind it, or even better is there a proof ...
0
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2answers
262 views

Advantages/Disadvantages of “hanging off” a motorcycle when leaning

The closest question I could find with regards to this subject was this one: Countersteering a motorcycle However, it does not address the specific physics of what I would like to know. There are 3 ...
0
votes
1answer
31 views

Vector representation of angular quantities?

In the world of pure rotation, a vector defines an axis of rotation, not a direction in which something moves. Does it means that angular quantities like angular momentum, angular speed, torque etc ...
2
votes
1answer
122 views

Physics of a cold and hot top

Imagine two tops made up of exactly one thousand atoms. One is kept at 4 degrees Kelvin, the other at room temperature. 1. Would they weigh the same given an arbitrarily precise scale in the Earth's ...
0
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0answers
14 views

Determining the range of values for separation angle (Landau problem)

I encountered a problem while reading the following exercise from the second Landau & Lifshitz volume: Determine the range value in the $L$-system for the angle between the two decay particles ...
2
votes
2answers
3k views

Rolling resistance and static friction

I am a bit confused about the relation between rolling resistance and static friction. I have often heard that it is the static friction that lets the wheel roll. Consider the following two cases: ...
1
vote
0answers
38 views

question regarding work energy theorem [closed]

The question says A smooth track in the for of a quarter circle of radius 6 lies in the vertical plane. A ring of weight 4N moves from $P_1$ to $P_2$ under forces $F_1$,$F_2$ and $F_3$. $F_1$ is ...
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0answers
6 views

Effective length factor of a polymer in solution

If one wants to calculate the force needed to buckle a polymer in solution with Euler buckling, what would the effective length factor be? The polymer is free to move and rotate in solution as it sees ...
5
votes
1answer
173 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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2answers
148 views

Instant centre of rotation for two connected gears

The two gears are have the angular velocities $\omega_1$ and $\omega_2$ respectively with respect to $Oxyz$. The task is to determine the angular velocity $\boldsymbol{\omega}$ of the arm ...