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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What is $Δf=ρ$ in Physics?

I asked a while ago a question on mathoverflow. It was a mathematical question with physical implications. To cut the story short, one mathematician said that Classically, a potential satisfies ...
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1answer
108 views

Differential holonomic constraints

Differential holonomic constraint is an integrable homogeneous first order differential equation: $$\sum_{i}\mathcal{E}_{i}(q)\frac{dq_{i}}{d\tau}=0;$$ in which $\sum_{i}\mathcal{E}_{i}(q)dq_{i}$ is ...
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2answers
78 views

energy of a ball [closed]

What is the energy of a ball lying on the ground at rest? As it is not in motion, it will have zero kinetic energy and as it is lying on the ground its potential energy will also be zero, taking the ...
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0answers
43 views

Is it proper definition of the free motion? The orbit of free motion is a free group [closed]

That's what I wrote in my notes but I don't understand this definition, I've studied group theory but free groups were not included. Can someone explain this definition, please?
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1answer
80 views

How does the height reached by a projectile of given flight time depend on air resistance?

Suppose we fire a cannonball straight up. We measure the duration of its flight and use that to estimate the height it reached. Does including air drag increase or decrease the estimated height, ...
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0answers
43 views

First problem from Slater & Frank book on mechanics [closed]

I can't solve the very first problem and have no one to help me (I'm self-studying it in these vacations): "1. A particle moves in a vertical line under the action of gravity and a viscous force ...
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1answer
24 views

Hamiltonian form: inverting the general momenta

I am studying analytical mechanics and am confused with the part about Hamiltonian form. My textbook develops the whole theory of Legendre transforms, in order to invert the formula ...
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2answers
49 views

Q factor of driven oscillator

In driven oscillator it can be explained by the following differential equation $$\ddot{x} + 2\beta \dot {x} + \omega_0 ^2x = A \cos(\omega t)$$ where the $2\beta$ is coefficient of friction, the ...
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2answers
108 views

Find the error: If $L_x$ and $L_y$ are zero, then $L_z$ is conserved

From Goldstein's Classical Mechanics (2nd ed.), problem 38 of chapter 9 basically says the following: It's been shown that the Poisson bracket of two constants of the motion is also a constant of ...
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0answers
22 views

Classical Mechanics Resources [duplicate]

I hope that my question doesn't violate the posting rules. I was wondering if any of you have any resources (websites, books, etc.) for classical mechanics. My first week of classical mechanics has ...
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0answers
45 views

Principle of Most Action? [duplicate]

In Landau-Lifshitz - Vol 1. Mechanics, right after the introduction of the principle of leas action, there is the following comment: It should be mentioned that this formulation ($S = ...
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1answer
47 views

Fluid dynamics question [closed]

Consider 2 cubes one resting horizontally with a hole at the bottom corner , we can say that the speed of water coming out of there is sqrt(2gh) if the hole is considerably small , what about the rate ...
2
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1answer
71 views

Conceptual problem with action considered as function of endpoints

I am having some trouble with understanding why it makes sense to consider action in classical mechanics as function of endpoints $q_{initial}, \ q_{final}$ and endtimes $t_{initial}, \ t_{final}$. ...
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60 views

Centrifugal force on body in motion in space

I'm trying to understand the motion of a body in space for simulation purposes and wondering if my understanding of centrifugal force is correct. Imagine a body in space with no gravitional/EM forces ...
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0answers
28 views

Why do very small balls attached to a tiny spring propel themselves in hardly moving fluids? [duplicate]

I recall watching a youtube video about a ball with a spring on the idea propelling themselves through stable fluids without any assistance, even if we make sure the spring isn't moving in the ...
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2answers
57 views

Deriving Hamilton's equation of motion

I am trying to derive Hamilton's equations of motion without using Lagrange's method but am left with an additional factor of $1/2$. Where am I going wrong? Please note this in not a homework ...
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1answer
33 views

Are there fifth-kind and sixth-kind generating functions?

In Goldstein's Classical Mechanics (2nd ed.), Section 9-1, pgs. 382-385, the generating functions (hereafter denoted $F$) for canonical transformations are introduced. From here on out, I'll refer to ...
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0answers
55 views

Which of Landau's books are suited for undergraduates? [closed]

Seeing how well-received Landau's books are, I want to know if any of them are suited for undergraduates.
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1answer
62 views

Independent canonical coordinate variables?

In Goldstein's Classical Mechanics (2nd ed.) on section 9-1 page 382, there is a discussion about finding a canonical transformation $(q_i,p_i)\rightarrow (Q_j(q_i,p_i,t),P_j(q_i,p_i,t))$ from a given ...
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2answers
97 views

What causes the balloon to pop when we push with needle onto it's surface?

I am a bit puzzled because I can see two possible reasons, first one is more common and the other one makes sense too, so here they go: 1) balloon pops because of the fact that after pressure is ...
9
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5answers
271 views

Momentum of slowly spinning (viscous) fluid

If we have a massless cylindrical container (or radius $R$) with a liquid of certain density $\rho$ and viscosity $\mu$ at rest. Then at time zero we impart a constant rotational velocity $\Omega$ on ...
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0answers
21 views

Ski treadmill materials

This ski treadmill is not much of an incline, but it still allows people to ski and carve out turns. What materials have such a low coefficient of friction, yet allow higher friction at higher ...
1
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1answer
42 views

When an object is moving at a constant velocity,would the normal force and $mg$ be equal?

Does the object's normal force and $mg$ cancel out, resulting in the two force becoming equal, or would one force be greater than the other? Thank you! Edit: Also would the $mg$ be considered weight ...
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19 views

Relation between solvent accessibility and brownian motion

Assume one has a molecule (made of nodes) inside a solvent. If one tries to model the average effect of the interaction between the molecule and the solvent, one has two effects: 1- Friction term on ...
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1answer
61 views

hard sphere collision condition with periodic boundary conditions

Hello Stack Exchange Physics, I am curious if there is an analytical or efficient numerical solution for the collision of hard spheres in a rectangular unit cell with periodic boundary conditions. ...
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0answers
21 views

Probability of light being refracted in deep space by H 2(Hydrogen)

Is it a valid question to ask what is the percentage of light that gets refracted by H 2 for a certain distance(Lets say 1 light year) in deep space. Lets assume a few(3) Hydrogen atoms per cubic ...
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35 views

When the equations of motion are not unique (eg. when they are given by eigenvectors), which will the free particle adhere to?

For this question I think it will be easier to express the usual equation describing the motion of a "free particle,"--viz. $g_{ij}\dot{x}^i\dot{x}^j$--in matrix form as follows: ...
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1answer
65 views

Is there really no transverse sound wave in air? [duplicate]

Everything has some viscosity. The viscosity of the medium may support transverse wave, right? So, is there really no transverse sound wave in air?
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4answers
70 views

Detached wheel from a moving vehicle speed

If a wheel is detached from a moving vehicle, would it speed be higher than the vehicle? Why?
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0answers
35 views

Maximum possible acceleration value on a ball in volleyball game

I have been examining this subject on web but could found enough information yet. I have to make a decision on choosing "range" for accelerometer which will measure acceleration value of ball in ...
1
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1answer
58 views

Experiment: releasing the copper bar above a permanent magnet

A classic experiment shows that when we drop a magnet through a copper coil long tube, there is eddy current induced in the coil. Then, due to lenz law, the motion of the magnet will be opposed and it ...
2
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1answer
42 views

Lagrangian of a block connected to a circular track [closed]

Could someone help me? I am having trouble with obtaining the same result in part b) for this problem: Using the Lagrange Equation with respect to $\theta$, I obtained ...
1
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1answer
35 views

Determining Height of Platform on Fulcrum

Consider this scenario: We have a platform resting on a fulcrum. The platform's tilt is controlled by a motor attached to 2 levers: Is the link between the height of the top of the lever ...
3
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2answers
85 views

Minimum initial vertical velocity of a projectile

A basketball is launched by a person with an initial velocity $v$ at an angle $\theta $ from a height $L$ into a basket of height $H>L$ which is a horizontal distance $d$ from the person. ...
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0answers
32 views

Pivot Point Equations [closed]

Assume we have a platform fixed to a pivot point: -Forgive the crude image- We use 2 rods, either side of the pivot point, but at different distances from it. If we were to lift ROD 1 by a certain ...
3
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1answer
72 views

Application of Euler-Lagrange equations (Trivial problem, instructive one)

I have some doubt about a really trivial and simple problem in which I have to use ELE. Supposing I have a pendulum, in which the rope is a spring, so it's length may change in time. I have a mass ...
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0answers
54 views

Acceleration in a space capsule which is falling to the earth [closed]

At first I apologize for asking such a career killing question in such an elite platform. Today I tried to prove something to four graduated engineers which I will mention below. The argument ...
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1answer
36 views

Expressing angular velocity of solid body [closed]

The problem: We have a circular disk of radius $R$ and mass $M$ that is mounted on a rotation axis that is not the axis of symmetry of the disk. The moment of inertia with respect to the axis of ...
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0answers
21 views

Does nature prefer second order differential equations? [duplicate]

We all know Newton's second law: $m \ddot{x} = F(x)$ or equivalently Euler-Lagrange or Hamilton's equations. In quantum mechanics the Schrödinger equation is also a second order differential equation. ...
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0answers
24 views

should transverse and longitudinal phonon velocities be equal for this mass spring system?

Let's say we have a cubic lattice of identical masses $m$, each connected to its 6 nearest neighbors by identical spring constants $k$. Essentially, the problem is I get an eigenvalue problem with ...
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1answer
29 views

An electron moving in a vacuumed chamber

Consider an object of mass $m$, e.g. an electron, moving in a straight line with constant non-relativistic velocity $\vec{v}$ in a vacuumed chamber, such that there are no collisions. Imagine the ...
3
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2answers
107 views

How mass is determined in dynamics?

Mass is one of the most core and complicated concepts in dynamics. I have tried many books but I still don't have a good idea of how the mass of any object is determined relative to another. In The ...
3
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2answers
105 views

If gravity dropped off with the cube of distance

If gravity, for instance, dropped off with the cube instead of the square of distance from the Sun, would the planets still follow elliptical paths?
1
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1answer
91 views

Why does the pen does not move straight?

If i put a pen on a table in its horizontal position and then i try to move it horizontally by giving it a small push, so that it would fall off a table, i expect it to move horizontally but my pen ( ...
3
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1answer
133 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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0answers
35 views

Stewart platform formulas [closed]

What kind of formulas/equations are commonly used to implement Stewart Platforms in electronics and mechanics? Using a co-ordinate system, how would you determine the position of each actuator, etc?
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0answers
25 views

compound bars in series

Compound bars 1 and 2 have lengths L1 and L2, areas A1 and A2, Young moduli E1, E2,thermal expansion coefficient a1 and a2. subjected to a change of temperature T. Two ends of the bar are fixed. The ...
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1answer
40 views

Composite bar in series paradox

2]2 Here is the progress and the problem that I encounter. I can calculate the tensile force but it seems like the force cannot exist in the first place ? P/s: I am sorry because I can only pose the ...
2
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1answer
53 views

Changing the length of a spring [closed]

Imagine we have a spring that is hanging from the roof with $k = 200$ and a stone with $ W=10N $ is pulling it down. Then due to $$ F=kx $$ we have $x=.05m=5cm$ Now we halve the length of the spring. ...
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32 views

Falling objects with different masses

I know that free falling objects with different masses fall at the same rate but that does not explain why objects with big masses are heavier to lift? what is gravity anyway I know it isn't a force ...