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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Motion Integrals of a Particle in a Force Field

I am trying to wrap my head around the following problem: A point particle is moving in a field, where its potential energy is U=-α/r. Find first motion integrals. In our university we have no ...
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67 views

Simple explanation of first and second class constraints with an example

Can someone give a simple physical example of first class and second class constraints? I mean, if you were giving a classical mechanics lecture for undergraduates, how would you explain this concept ...
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Symplectic structure and isomorphisms

In his book Mathematical Methods of Classical Mechanics, V.I. Arnold writes To each vector $\xi$, tangent to a symplectic manifold $(M^{2n},\omega^2)$ at the point $\mathbf{x}$, we associate a ...
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Trajectory of a boat given by $$r=\frac{d sec(\alpha)}{(sec\alpha + tan\alpha)^{V/V_{R}}}$$ [closed]

I need some help with this problem, I've tried using polar and cartesian coordinates but I dont know how to get the trajectory (I've already obtained the position, velocity and acceleration vectors as ...
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19 views

Non-dimensionalizing the “bead on a rotating hoop, with viscous damping” problem

This is not a homework question. Rather, this is an exercise I have taken up on myself. In particular, I am trying to find an algorithmic way to non-dimensionalize known equations, using the ...
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38 views

Does this massless spring affect the system?

I have to write out the differential equation modelling this system: There's a mass connected to a wall with a spring of spring constant $k_1$, sitting on a frictionless surface, with another spring ...
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29 views

Rotation of Thin street sign

I am attempting to complete a home question in which a shop sign in the shape of a thin rectangle of size p x q (with q being the longer side), and mass m, that rotates about an axis that passes ...
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1answer
41 views

Limits for the linear wave equation

In acoustics and continuum mechanics the following wave equation (for Speed of Sound $c$) for the pressure field $p$ is well-known: $\partial_t \partial_t p = c^2 \Delta p$. This wave equation can be ...
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How could a cord withstand a force greater than its breaking strength?

How could a 100 N object be lowered from a roof using a cord with a breaking strength of 80 N without breaking the cord?? My attempt to answer this question is that we could use a counter weight. But ...
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2answers
65 views

Energy drain in damped oscillator

Suppose we have a mass on a spring with a damping term. The equation of motion is given by: $$m \ddot{x} = -kx - c\dot{x}$$ I believe solutions are damped oscillations of the form: $$x = x_0 ...
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1answer
83 views

Mathematical pendulum in accelerating frame of reference [closed]

An aquintance of mine, who is a first year physics student was given a simple task as a homework-like task, which is about determining the ratio of periods between two equal-parameter mathematical ...
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2answers
108 views

Taking moments about two different points in a system of forces

If you have a system of forces and you take moments about two different points will the moment be the same?
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1answer
29 views

Is the force of a lifting arm due to a piston an internal force?

When I was analyzing an excavator, I was wondering if the force that the piston exerts on the lifting arm is an internal or external force. I am a bit confused because the geometry of the system ...
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153 views

How the center of gravity works in the picture? [duplicate]

How the center of gravity works in the picture? How the other parts of the body able to hold the bal;ance of the center of the gravity of the man?
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42 views

Derivable Concepts in Mechanics and Electromagnetism

In Classical Mechanics, one of the possible foundations is based on three concepts aka mass(equivalent to energy), length and time. This is a foundation because we can model everything ( pressure, ...
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43 views

Prove a transformation is a variational symmetry?

My question: How to prove the family of transformations of the $(t,q)$ space, given by $(t,q) \to (t,U(\epsilon)q)$, where $U(\epsilon) \in SO(3)$, is a variational symmetry? So it depends on $L$ by ...
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107 views

Deriving Snell's law via Lagrangian mechanics

A particle moves with kinetic energy $K_1$ in a region where its potential energy has a constant value $U_1$. After crossing a certain plane, its potential energy changes discontinuously to a new ...
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3answers
105 views

Can vertical SHM occur in a system of a mass between 2 springs between 2 vertical pillars? [closed]

The problem is detailed above. I have worked through problems involving SHM in the horizontal plane, but unsure how to go about it vertically. I know the weight component would need to be ...
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1answer
48 views

Why ingoing and outgoing impact parameters equal in elastic scattering?

Take the Rutherford scattering, as for example in this picture: What is the easiest way to show that the impact parameter "b" (see picture) is the same for the ingoing and outgoing trajectories? ...
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98 views

Chocolate dynamics

Now I have found a possible model on how to describe chocolate when it is chewed. It has to do with geometrical transformations when a curve $\gamma$ intersects a manifold $M$. The chocolate is ...
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24 views

Will the center of mass of the whole system change when object swims on curved surface?

In the example given here, the object can move on the frictionless surface of the sphere by changing its shape periodically. So will the center of mass of the whole system change after the object ...
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42 views

Force in colliding snooker balls

If a snooker ball is traveling at 2m/s and hits another ball, the first ball will stop dead and the second will accelerate instantaneously to 2m/s. F=ma, so this would seem to imply an infinite force. ...
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2answers
76 views

How to calculate the classical on-shell action for a harmonic oscillator? [closed]

So, short and sweet, I've been reading the path integrals book by Feynman and Hibbs, and one of the elementary problems they ask is to calculate the classical on-shell$^1$ action of a harmonic ...
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49 views

Rheological behavior of chocolate

If someone eats chocolate, the chocolate goes through the following configurations: $\chi_0:$ chocolate is solid and has a smooth Surface everywhere; the Riemann Tensor vanishes on every Point of the ...
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1answer
49 views

How to calculate the deceleration of two trains moving with the same velocity? [closed]

Two trains travelling on the same track are approaching each other with equal speeds of 40m/s. The drivers of the train begin to decelerate simultaneously when they are just 2km apart. If the ...
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2answers
87 views

How was time defined before we knew the speed of light was constant or in classical physics? [closed]

Nowadays, we now about $c$ the universal speed of light. This lets us define the notion of distance in terms of time (despite the fact that it works the opposite way for our common units.) Before ...
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1answer
87 views

Why Galilean spacetime is not $\mathbb{E}^4$?

In Newtonian mechanics the physical spacetime is a Galilean spacetime with an affine surjection $\pi : \mathbb{A}^4\to \mathbb{E}^1$ from affine space $\mathbb{A}^4$ to Euclidean space $\mathbb{E}^1$. ...
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74 views

How is this a gauge choice mathematically?

I've been reading an article about the "square cat", which is described as the system bellow Such system is a deformable body that can change $a$ and $\theta$ but has $b$ fixed. The article uses ...
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2answers
129 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 ...
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2answers
148 views

Hockey puck collision [closed]

I have a homework question in which a sticky hockey puck traveling at constant velocity parallel to the side of the rink strikes a stationary puck and sticks to it. The angels between centres at ...
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1answer
86 views

Does the moment of inertia change?

I am currently working on a practice problem for my upcoming exam and I have difficulties getting my head around moment of inertia. If the ball has mass $m$ and is going around in a circle with ...
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51 views

Time reversed Abraham-Lorentz reaction force

The Abraham-Lorentz radiation reaction force on a charged particle is given by: $$\mathbf{F_{rad}} = \frac{q^2}{6\pi\epsilon_0c^3}\mathbf{\dot{a}}$$ I understand the situation where one fires a ...
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1answer
165 views

How much force can bolt cutters exert?

What's the mechanical advantage of an ordinary, let's say, 3 feet long bolt cutters? How many pounds can they exert? I'm asking because I have a lock which is apparently immune to over 9 tons of ...
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97 views

A question on Lagrangian dynamics an the velocity phase space

I've struggled in the past with understanding why we can treat position and velocity as independent variables in the Lagrangian, but I think I may have finally become a bit more enlightened on the ...
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44 views

Quantum chaos vs classical chaos

There is this popular conjecture from Bohigas, which says: When the analogeous classical system of a quantum system shows chaotic behaviour then the spacing distribution of the quantum system ...
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1answer
71 views

Jumping vs pulling my hair upwards

Why can't I jump or fly if I pull my hair upwards, while I can jump using my legs? The way I see it, when jumping someone lifts its body using the muscles in the legs (while the feet are standing ...
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1answer
58 views

What is the criterion for a change to be adiabatic?

I'm trying to understand whether the change of a parameter $\lambda$ of a Hamiltonian $H$ is adiabatic. Reading Landau and Lifshitz "Mechanics", I see ... let us suppose that $\lambda$ varies ...
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235 views

When can phase trajectories cross?

It's said in elementary classical mechanics texts that the phase trajectories of an isolated system can't cross. But clearly they can, for example for the pendulum, the trajectories look like this: ...
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1answer
121 views

Falling charged objects: energy conservation paradox?

Imagine that we start with two oppositely charged objects on the ground, separated by a distance $d$, with charges $+q$, $-q$ and masses $m$. We raise them both up to a height $h$. In doing so we ...
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2answers
201 views

Natural Frequency of an object and the phenomenon of resonance!

I have read about the term natural frequency in quite a lot of places. But I haven't found an explanation as to what is vibrating. It was pretty awkward when I couldn't clearly answer my little sister ...
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31 views

Locally accessible dimensions of configuration space

I am reading a book called "Structure and Interpretation of Classical Mechanics" by MIT Press.While discussing configuration space and degrees of freedom,the authors remark the following: Strictly ...
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54 views

Magnetic Field and Flow of Vector Potential

I am sorry, when my question is not really concrete, but here we go. Consider the Hamiltonian function $$H(x, \xi) = \frac{1}{2m}\bigl|\xi - eA(x)\bigr|^2$$ corresponding to a charged particle in a ...
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1answer
84 views

Lagrangian mechanics and initial conditions vs boundary conditions

It bothers me that many basic books on the classical mechanics don't discuss the following difference between "Newton's laws" and the "Principle of stationary action". Newton's laws can predict the ...
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2answers
42 views

On the isotropy of materials

Good morning. I am working on Honeycomb structures and first of all I would like to understand whether it is Isotropic or not, and , if the latter holds which kind of anisotropy it has. How to do it? ...
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3answers
96 views

Classical Limit of the Quantum Harmonic Oscillator

The classical harmonic oscillator obeys an arcsine law in that the distribution of positions of the particle over a single time cycle is proportional to $\frac{1}{\sqrt{A^2-x^2}}$, $A$ being the ...
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1answer
67 views

Is Liouville's theorem valid for dimensionally restricted systems?

Liouville's theorem states that the phase space volume of a system is conserved over time. Intuitively, this seems to imply that if a system is at some time constrained to, say, a curve in phase ...
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2answers
76 views

Does sound have a “louder” direction?

I have a question about the propagation of sound waves. We have two TV's in our house that are almost right on top of each other. One is located on the first floor and the other one is located on ...
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2answers
77 views

Calculating the flex of a solid bar under force

I want to calculate how much a solid bar will flex when force is applied to it. The set up looks like this: The rod (in green) rests on two stationary points, and the force is applied in the center ...
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2answers
47 views

Can center of mass move without any force?

For instance, consider a weight on one end of the ring. Assume that the ring has negligible mass compared to the weight. When the weight splits into two, moves around the ring and recombines at the ...
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350 views

Why does the Stern–Gerlach quantum spin experiment conflict with classical mechanics?

My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that ...