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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Liouville's theorem and preservation of topology

What might be a simple proof showing that the time evolution of the phase space volume can't lead to splitting off of the phase space volume? By Liouville's theorem, the total phase space volume is ...
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0answers
37 views

The classical hydrogen atom

Suppose we want to analyze a hydrogen atom using purely classical mechanics. This obviously is not exactly how things work - quantum mechanics plays a huge role and probability distributions are ...
4
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1answer
93 views

Any good resources for Lagrangian and Hamiltonian Dynamics?

I'm taking a course on Lagrangian and Hamiltonian Dynamics, and I would like to find a good book/resource with lots of practice questions and answers on either or both topics. So far at my university ...
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0answers
14 views

Strain-Displacement relationship symmetrization

In the context of infinitesimal elastic strain theory, one writes the relationship between displacement and strain as $$ \epsilon_{ij} = \frac{1}{2}( \frac{\partial u_i}{\partial x_j} + ...
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0answers
30 views

Action principles and covariant equations [duplicate]

Can every physically sound differential equation, that is covariant, deterministic etc. be derived by extremising a suitable action using a suitable lagrangian, that may be arbitary. Is this a ...
33
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14answers
3k views

Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
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3answers
2k views

Normal force of loop-the-loop at the side of the circle

In the loop-the-loop ride a car goes around a vertical, circular loop at a constant speed. The car has the mass of 230 kg and moves with the speed of 300 m/s. The loop-the-loop has a radius R=20 m. ...
4
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1answer
111 views

Poincaré maps and interpretation

What are Poincaré maps and how to understand them? Wikipedia says: In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is ...
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5answers
234 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. ...
10
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1answer
424 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: ...
6
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1answer
82 views

Movement of a cylinder filled with water

Not long ago I was pretty bored at a dinner and I started playing with a water bottle that was not empty: I've been quite interested in its behavior when putted on its side and pushed: the bottle of ...
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2answers
56 views

What is the percentage of energy recovery in Kinetic Energy Recovery Systems(KERS) in cars?

Kinetic Energy Recovery Systems (KERS) use flywheels to recover energy from the kinetic motion of cars. They use a rotating flywheel that generates energy as it rotates- this generates the electric ...
0
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1answer
65 views

Landau Mechanics equation 16.9

I am having trouble deriving the equation 16.9 from Landau's Classical Mechanics book. This equation is the maximum kinetic energy of a particle if a massive particle with mass $M$ disintegrates into ...
11
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4answers
350 views

Non-linear systems in classical mechanics

In general, what is meant by non-linear system in classical mechanics? Does it always concern the differential equations one ends up with (any examples would be greatly appreciated)? If so, is it ...
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0answers
62 views

Chaotic behaviour re-obtained in QM

In classical mechanics, when we talk about chaotic systems (e.g. double pendulum), we always associate (or justify) them with the non-linearity(and non-integrability) of the differential equations ...
0
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1answer
19 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
54 views

Conservative force as a potencial energy gradient

A conservative force $\vec{F}$ is apparently defined as the gradient of a potential energy $U$: $$\vec{F} = -\nabla\ U$$ I am curious if this definition was originally used to describe a ...
0
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0answers
10 views

Find the SHM time interval [closed]

Parts i) and ii) I can solve. But for part iii) I can't do, as I don't know which equation describes the SHM motion? Is it $y=0.5sin(1.2t)$ or $y=0.5cos(1.2t)$ or $x=0.5sin(1.2t)+2.5$? I thought ...
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2answers
41 views

Complexity of a physical system

Are there any accepted definitions quantifying the complexity of: a) macroscopic, classical mechanical systems (e.g., a bicycle) b) microscopic systems (ensembles of atoms)? By the way, I'm not ...
0
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1answer
46 views

Equation for Terminal Velocity on an inclined plane and the time it takes to reach it

Now I'm doing a research on the matter similar to this thread : Terminal Velocity of identical shape/size objects which is very self explanatory and very helpful. However in my case, the objects will ...
3
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1answer
52 views

Non-deterministic particle system

This question is in the spirit of Norton's dome, an example of an apparently non-deterministic system in Newtonian mechanics. Under certain restrictions, the Picard–Lindelöf theorem guarantees the ...
0
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1answer
49 views

How can I determine whether motion is uniform and continuous? [closed]

I am just starting to take Physics, and I don't have any Physics from high school.
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2answers
30 views

Isolated and non-isolated systems: Momentum?

I'm having a difficult time understanding why two billiard balls colliding is an isolated system, yet a car crashing into a wall is a non-isolated system. Does it really only have to deal with the ...
0
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2answers
31 views

If a mass $m$ whirls with constant speed $v$ at the end of a string of length $R$, what is the force on $m$ in the absence of friction or gravity? [closed]

This problem appears in a book I'm reading. The solution is given as follows: The only force on $m$ is the string force $T$ which acts towards the center. The radial acceleration is $a_r = \ddot r ...
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2answers
55 views

Pulling on a weakened rope - where will it tear?

Let's say I have a rope of 10m length and it is weakened in 3 spots: at 2.5m, at 5m and at 7.5m. Weakened means that if enough tension is applied it will tear at these points (all points are equally ...
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1answer
42 views

How to reconcile these two approximations?

I'm working on what should be a simple problem (Taylor Classical Mechanics problem 6.23. Not homework.), but I'm having a tough time reconciling the many ways it can be tackled. An aircraft whose ...
11
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3answers
236 views

What could cause an asymmetric orbit in a symmetric potential?

My question can be summarized as: Given a potential with a symmetry (e.g. $z\rightarrow-z$), should I expect orbits in that potential to exhibit the same symmetry? Below is the full motivation for ...
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2answers
39 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, ...
5
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5answers
914 views

How does an object's motion behave if dropped from an aeroplane travelling diagonally upwards?

Imagine an aeroplane travelling with velocity $v$ at some angle $\alpha$ from East to North. A box is dropped from the aeroplane. What would the projectile of the box be? Would it be a parabola with ...
20
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4answers
1k views

Phase space volume and relativity

Much of statistical mechanics is derived from Liouville's theorem, which can be stated as "the phase space volume occupied by an ensemble of isolated systems is conserved over time." (I'm mostly ...
0
votes
1answer
66 views

What indicates if object will be reflected - certain example

If I throw a small rock(1kg) at a big rock(100kg) the small rock is reflected; Let's say my weight is 80kg - if I would jump into a big rock instead of being reflected I would move in the same ...
1
vote
1answer
66 views

Two masses on frictionless table with one string connecting both masses on ground and the other string [closed]

From Morin's Introduction to Classical Mechanics page 342: A solid cylinder of mass $m$ and radius $r$ lies flat on frictionless horizontal table, with a massless string running halfway around ...
0
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0answers
11 views

Robot speeds in body frame

I am building a robot with two wheels (and differential drive) and I am trying to make it have the same performances over very different loads (an order of magnitude between the ), so I decided to try ...
1
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2answers
96 views

How can I derive the Hamiltonian of simple harmonic oscillator from this Lagrangian?

I'm working through Leonard Susskind's Theoretical Minimum: Classical Mechanics and I can't seem to understand how the Hamiltonian of a simple harmonic oscillator is derived from the following ...
0
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0answers
39 views

Should the liquid come out of the tank if a hole is drilled in the vertical wall?

This is a tank filled with water kept on ground. The points $A$ and $B$ are at 'same horizontal level', hence, as per an interpretation of pascal's law, pressure at $A$ must be equal to the pressure ...
2
votes
1answer
181 views

Classical models with unbounded particle number

Is there any classical model which deals with the birth, life and death of particles? What application could it have? I am talking about a 'billiard-ball' kind of model, but the kind in which balls ...
1
vote
1answer
42 views

Shock-waves, Bangs and the Speed of Sound

I was watching this video of an erupting volcano. Some Guys in the comments tried to estimate how far away the volcano is by using the delay until the "shock-wave" hits the camera and the speed of ...
0
votes
1answer
18 views

belts and balls, correct size of holes

I'm working on a robot that has to transport a set of balls up at a 60 degrees angle. In order to do this I want to use a belt system with holes in it. Now my question is how big do these holes have ...
2
votes
1answer
46 views

Experimental set up of vertical circular motion

We are trying to do the following experiment: http://farside.ph.utexas.edu/teaching/301/lectures/node90.html. At the moment, here is the experimental setup: We have a rod 0.4 m long which rotates ...
9
votes
1answer
218 views

Cutting a circle and moving endpoints

A metal (or otherwise, suitably elastic) circle is cut and the points are slid up and down a vertical axis as shown: How would one describe the resultant curves mathematically?
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0answers
26 views

Modeling the creation of transverse waves

Suppose I hang one end of a jump rope against a wall and start waving the other end. I'm interested in knowing the behavior of the jump rope as it starts generating waves. In other words, how can I ...
0
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0answers
21 views

Unbalancing a system of rotating masses - what happens?

Lets say you have a rod spinning on its long axis and this rod has a few smaller beams attached perpendicular to the rod at varying angles and with varying masses. Here's a picture from wikipedia to ...
0
votes
2answers
49 views

How to take in to account torques applied at different points

Suppose we have a rigid body with known moment of inertia through some axis ($J$) and that there are multiple torques being applied in different points in that body. I know that for a rigid body, the ...
3
votes
1answer
258 views

Hamilton-Jacobi equation with time dependent Hamiltonian

I was struggling with this exercise about Hamilton-Jacobi equation. I have to solve by menas of Hamilton's principal function the system with Hamiltonian: $$\tag{1} H=\frac{p^2}{2m}-mAtx $$ with $A$ ...
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0answers
20 views

Example of materials with 21 independant coefficients in linear elasticity?

By definition of linear elasticity, the strain et stress tensors are related: \begin{equation} \boldsymbol{\sigma}=\mathbf{C}:\boldsymbol{\varepsilon} \end{equation} and because of minor and major ...
2
votes
0answers
22 views

Hysteresis in liquid–solid-phase transitions such as Agar

I'm wondering how it is possible for a substance to have a significantly different melting point than its freezing point. What physical interaction "locks" a substance such as Agar into the phase that ...
0
votes
2answers
812 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 ...
2
votes
1answer
100 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 ...
2
votes
3answers
86 views

Unstable equilibrium in a pendulum

Consider a pendulum with a bob and a massless, rigid, hinged rod attached to the bob. The bob is at rest at the bottom most position. Neglecting friction, is it possible to impart such a velocity ...
1
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0answers
35 views

how to draw mechanical engineering problems [closed]

Hello I'm not entirely sure if this is on topic, but does anyone know software (or methods) to draw mechanical engineering schematics? (For statics/dynamics, so things like beams joints, rollers, ...