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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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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40 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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352 views

Inertia of yo-yo goes to infinity, what is tension and acceleration?

For this part, imagine that the string is wound around the center axle of a yo-yo; the axle radius is Raxle, but the yo-yo casing has a radius Rcasing≫Raxle and moment of inertia I≫mr2axle. In the ...
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125 views

Problem with derivation of phonons in crystal

In this derivation of phonon solutions, everywhere, we are forcefully assuming the wavelike characteristics along the length of the chain. While all we can deduce for finding out the fundamental ...
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44 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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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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2k views

Potential energy from opposing magnets repelling each other with a gap of 1 mm

I have two powerful rare earth magnets, that are separated by a distance of 1 mm. I applied energy to bring them closer to each other, hence increasing the potential energy. Now, when one of the ...
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1answer
62 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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1answer
39 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 ...
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58 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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474 views

Hamiltonian function for classical hard-sphere elastic collision

I'm trying to find the Hamiltonian function for a system consisting of a single particle in one dimension colliding elastically with a wall at $x = 0$. Everything I've read on the topic (e.g. this ...
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2answers
53 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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2answers
146 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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26 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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42 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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28 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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4answers
204 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 & ...
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2answers
66 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 ...
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161 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, ...
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14 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 ...
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1answer
48 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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1answer
29 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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74 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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17 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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Hamiltonian is conserved, but is not the total mechanical energy

I wondering about the interpretation for the energy difference between the Hamiltonian and the total mechanical energy for systems where the Hamiltonian is conserved, but it is not equal to the total ...
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19 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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264 views

Clearing up confusion about calculating torque

Suppose you have a shape consisting of two perpendicular rods (the whole shape is a rigid body) which stands upright so the plane of the rods is perpendicular to the plane of the ground, and the ...
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34 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
54 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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3answers
120 views

How much energy does it take to simply run forward?

I'm interested in tracking as much data about my runs as I can in an effort to get faster, and while I can easily estimate energy expenditure during an uphill run due to the change in elevation, I ...
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4answers
53 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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31 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 ...
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1answer
42 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 ...
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326 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 ...
2
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1answer
38 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 ...
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2answers
428 views

Classical Rutherford scattering (partial) derivation

I am having trouble answering the following question, please could you help! Thank you in advance for any assistance you can give. Consider classical Rutherford scattering of a particle with mass $m$ ...
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1answer
30 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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1answer
58 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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24 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 ...
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46 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
30 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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20 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
28 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
97 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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1answer
327 views

A different proof for 6 degrees of freedom

I want a different proof of 6 degrees of freedom of a solid object made of $N$ particles. I am thinking along these lines: The definition of rigid body is $$\left\lvert \vec{r_i}-\vec{r_j} ...
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6answers
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Degree of freedom paradox for a rigid body

Suppose we consider a rigid body, which has $N$ particles. Then the number of degrees of freedom is $3N - (\mbox{# of constraints})$. As the distance between any two points in a rigid body is fixed, ...
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2answers
100 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?
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88 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 ( ...