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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How to derive kinetic energy from the Lagrange equations? [duplicate]

I'm having trouble deriving the kinetic energy from the Lagrange equations. For reference, I'm following Landau and Lifshitz book, "Mechanics," which can be found for free at Archive. In any case, ...
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Einstein-Infeld-Hoffman-Lagrangian for a Test-Particle as Limit of Schwarzschild-Geodesic

Consider a test particle of mass $m$ which is in orbit around a spherical-symmetric body with mass $M$. It therefore has a position as described by the coordinates $r,\phi$, and its motion can be ...
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15 views

Pressurizing a circular toroidal shell

Consider a toroidal elastic, isotropic, homogeneous shell with a circular cross-section that is initially not pressurized. Under an internal pressure $p$, the shell might become more straight, but the ...
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1answer
64 views

Wave equation in classical mechanics!

We represent the wavefunction of any wave on the string as $$y=f(x-vt),$$ where $v$ is velocity of the wave and $x$ is distance from origin and $t$ is time taken to reach the given point and $y$ ...
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56 views

Classical Limit of Schwarzschild Metric

The orbit of a test particle orbiting a black hole can be described by the Lagrangian $$\mathcal{L} = -\frac{1}{2}\left(-\left(1-\frac{2 G m}{c^2 r}\right) \dot{t}^2 + \left(1-\frac{2 G m}{c^2 ...
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In the Principle of Least Action, how does a particle know where it will be in the future?

In his book on Classical Mechanics, Prof. Feynman asserts that it just does. But if this is really what happens (& if the Principle of Least Action is more fundamental than Newton's Laws), then ...
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32 views

How the mechanical equivalent of heat is employed in this situation?

Reading a little about the "mechanical equivalent of heat" what I understood is that we can convert units between calorie and $J$ by setting $$1\mathrm{\ J} =4.1860 \mathrm{ \ cal}.$$ Now, I saw a ...
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41 views

water stream cut off abruptly; why there will occur sprinkling?

Suppose that water flows with constant velocity $V$ and constant pressure $p$ through a pipe with diameter $d$. Now the pipe is suddenly cut such that the water will splash out of the pipe into the ...
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814 views

Force needed to push a syringe plunger: does one add force associated with downstream back-pressure to frictional plunger force?

I am trying to figure out how much force $F$ is needed to push a syringe plunger. The plunger needs to overcome the friction force $F_1$ and (a much smaller) inertia force $F_2=ma$, giving the total ...
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152 views

What happens to the coefficient of friction as the normal force increases?

Does the frictional force increase as the normal force increases, or does the coefficient of friction get smaller in value?
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1answer
60 views

Torque and Force of Pulley fixed on side

If you had only 1 pulley that is connected to a rotating shaft, and which has a rope circled around it once, with a mass M on one side and with the rope fixed on the other end, how would you then ...
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1answer
136 views

A mass hanging under a table: a problem from Goldstein [closed]

I'm trying to solve Problem 1.19 from Goldstein's Chapter 1 (2nd edition), and am getting bogged down in trigonometry (?). Please help me figure out what I'm doing wrong! Two mass points of mass ...
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215 views

Connection between Hamiltonian version of the least action principle and probability amplitude in the Schrödinger equation

If I'm not mistaken, Schrödinger was influenced to look at wave equations because of de Broglie's assertion about particles having a wavelength. He started with the Hamiltonian equation which is ...
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1answer
50 views

What to do when you're hit by another car? [closed]

I have a question about what's the "best" thing to do if you're about to be hit by another car. Imagine you're in your car, and you're at rest. There's another car coming at you, and they're going ...
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25 views

Computing the value of an Action given some boundary conditions

Having being dealing with Actions for a while I have come across a question in which I am required to calculate the value for $S$ an action in the form of a function for some given boundary ...
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1answer
701 views

Confusions about rotational dynamics and centripetal force

I am a high school student. I am having confusions about the centripetal force and rotational motion . I have known that a body will be in rest or in uniform velocity if any force is not applied. But ...
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1answer
119 views

What is difference between anisotropy and inhomogeinity of this type of composite material?

I am studying some types of composite materials having 2 phases - fibers and matrix. I have some questions and confusions. Any help is appreciated. The composite has fiber along length and I am ...
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Maximum speed of a rocket with a potential of relativistic speeds

Ultimately, the factor limiting the maximum speed of a rocket is: the amount of fuel it carries the speed of ejection of the gases the mass of the rocket the length of the rocket ...
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Invariance of Lagrange on addition of total time derivative of a function of coordiantes and time

My question is in reference to Landau's Vol. 1 Classical Mechanics. On Page 6, the starting paragraph of Article no. 4, these lines are given: If an inertial frame $К$ is moving with an ...
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1answer
87 views

Difference between phase space and Hilbert space? [closed]

Why is the phase space of classical mechanics not a vector space, but Hilbert space of QM is?
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714 views

Constraints of massive relativistic point particle in Hamiltonian mechanics

I try to understand constructing of Hamiltonian mechanics with constraints. I decided to start with the simple case: free relativistic particle. I've constructed hamiltonian with constraint: ...
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1answer
111 views

Quantum systems without a classical analogue? [closed]

I am now reading the quantum mechanics textbook by Dirac (chap. 4, $\S21$, p. 88). He says that his quantization procedure does not include all possible systems in quantum mechanics and there are ...
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207 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 ...
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1answer
39 views

Atmospheric pressure below sea level

If I go up in the air the amount of oxygen decrease and the atmospheric pressure gets lower. What would happen if i dig a hole 100 km down? does atmospheric pressure go up? when is the pressure so ...
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The coffee ring effect

Would spin coating a homogeneous solution of colloids also result in a coffee ring structure? Or is it just naturally drop casted evaporation methods that lead to the same.
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1answer
23 views

Can cyclic acceleration/deceleration be worse for fuel consumption?

Recently I have started to drive my car slower on the highway in order to save money on gas. However, I feel like I am spending at least as much fuel as before. One possible explanation that I thought ...
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2answers
158 views

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

An ion moves along the x-axis of a black box with a speed $V$ and returns in a time $$T=a V^b$$ where $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of a field ...
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Does vehicle tire mass effect efficiency?

This question has an interesting origin: A tire salesman was recommending tires (aka tyres) for a highly fuel-efficient vehicle. He said the vehicle was light (compared to most production cars), and ...
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1answer
34 views

Does a ball thrown down exert less force on the ground when we walk? [closed]

Scenario A: You stand still and throw a ball vertically down. When the ball hits the ground it exerts a specific force on the ground. Scenario B: While walking you throw a ball vertically down. When ...
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14 views

Isolated system and mutual interaction potential

We know that the total linear momentum of a closed (isolated) system is conserved due to homogeneity of space (Landau and Liftshitz, page 15, Mechanics). Hence for an isolated system of two bodies ...
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1answer
57 views

How can we tell the potential from the orbit?

The orbit is $$r(θ) = a(1+\cos θ).$$ The orbit of the particle is in polar coordinates. How can we tell the potential $U(r)$ from this? $U(r)$ goes to zero at infinity.
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1answer
59 views

Cylinder rotating without slipping on an accelerating slab [closed]

I am very confused by the following problem asked in my first year physics class: Please let me know if you can assist in any way! I've spent hours and hours on this question and gained absolutely ...
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30 views

Relation between linear and rotational motion of molecules?

The temperature of a substance, such as an ideal gas, can be related to the root mean square speed of the molecules. For example, for gases the molecules travel at about 480 meters per second. If we ...
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3answers
100 views

Conversion of angular momentum to linear momentum in free space

If two objects both with angular and linear velocity collide in free space, can the total linear velocity of the objects increase at the expense of a loss in angular momentum? In other words, imagine ...
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35 views

In what cases do we use the Routh Function? [duplicate]

As many of you, I studied Lagrangian Mechanics and Hamiltonian Mechanics, with the so famous functions called Lagrangian $\mathcal{L}$ and Hamiltonian $\mathcal{H}$ related by: $$\mathcal{H}(q_i, ...
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30 views

What is the displacement between highest points on a pendulum with discontinuous forcing? And is this dependent on gravity?

I know the question is worded horrendously, but my professor gives strange badly worded problems, so I've started to speak that way. It'll take a paragraph to pose this question properly. Consider a ...
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1answer
38 views

How do I calculate the work done on standing an object upright?

So I was trying to figure out how much work someone does when they do a sittup or crunch. I guess to make things simple, I'm imagining a really really thin rod with some uniform mass lying on the ...
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5answers
189 views

Is this a fundamentally relativistic phenomenon?

This question was inspired by some silliness in other threads but is independent of that silliness. Say that a train car sitting on a track is accelerated uniformly along its length if each point on ...
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2answers
140 views

Calculating how a polygon bounces off a plane

I'd like to calculate how polygons bounce off a plane. In this picture, the square doesn't bounce straight up, but instead it bounces somewhat to the right and starts spinning. But I have no idea ...
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0answers
29 views

General approach to Mechanics? [duplicate]

So, I know that this question may be tough to answer, but I am asking this question in all seriousness, and I don't consider myself a newbie... Lately, I am trying to find a way to "generalize" my ...
4
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1answer
90 views

When does the principle of superposition apply?

I assumed from my general physics courses that the principle of superposition was just an empirical fact about forces. Then I could understand that derived quantities like the $E$ and $B$ fields ...
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22 views

Which are the path variables in an intrinsic coordinate system?

This question concerns "path variables" or "intrinsic coordinates" or "normal and tangential coordinates" whichever you like to call it, in 3D. We have the three $path~~variables: ...
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1answer
146 views

Casimir Invariants of the Galilean group

I had studied a couple of things about Galilean and Poincare group. But in the Galilean group, there is not enough clarity on how to calculate generators for boosts ($B_i$), which if I do it seems I ...
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4answers
99 views

Measuring force of a punch

I'm trying to build a device that can mesure the force of a punch. ​ My initial plan was to build a platform with 4 springs (one at each corner) and an accelerometer in the middle. But, if the ...
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118 views

Matrix Representations of Galilean group

The general group element (in the vector representation) $$ \left [{ \begin{array} {c} \bar x^1 \\ \bar x^2 \\ \bar x^3 \\ \bar t \\ 1 \\ \end{array} } \right] = \left[ ...
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41 views

Good books for understanding Lagrangian formulation of classical fields?

I want to understand Lagrangian formulation for classical fields and apply it to understand constrained dynamics. Currently I am referring to "A modern approach: Classical Mechanics" by ECG Sudarshan, ...
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2answers
58 views

Can we measure the exact position and momentum of a ball by hitting it with other balls?

Imagine a billiard table that's is covered we can't see what's happening under the cover. Now imagine we throw in a ball whose throw in time, mass, size, position and velocity is unknown. To measure ...
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1answer
37 views

Note and homework organization [closed]

this is my first post here so please forgive any errors! I am currently in a mechanics class and having a little trouble trying to figure out how I should structure my lecture notes and my homework. I ...
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1answer
65 views

Is the Impulse-Momentum Theorem True? [closed]

This is just a general question I want to throw out there, and see arguments from both sides... Is Impulse-Momentum Theorem True? Well in my opinion I would say yes because it is a derived equation: ...
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Energy-Momentum tensor for classical field with nontrivial boundary conditions

Question: Is there a energy-momentum tensor for the potential flow equations with a free surface under the action of gravity (ie the equations governing some types of surface water waves)? ...