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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2answers
269 views

Momentum of transverse waves on a string

In general, if a wave carries energy density $u$ with velocity $v$, it also carries momentum density $u/v$. I've seen this explicitly shown for electromagnetic waves and (longitudinal) sound waves. ...
-4
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0answers
23 views

Derivative of an integral help [on hold]

OK, I lied a bit. It's not JUST the derivative of an integral. It's the derivative of a cosine of an integral. Solving the problem of the motion of a simple pendulum under a gravitational field using ...
3
votes
2answers
3k views

degree of freedom of a rigid body 5 or 6?

I'm confused here. I have a three particle (rigid) system. What would be the degree of freedom? I found out five. 3 coordinates for center of mass and 2 for describing orientation. But we have only ...
0
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0answers
34 views

Determining the Lagrangian of a double pendulum

Ok, I'm reading up on Lagrangian mechanics, and there is a problem that I don't really understand: the double pendulum (in this case, without a gravitational field). So, I want to take it step by step ...
0
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1answer
25 views

Energy Transferred to a Spring by a Time Dependent Force (using Fourier Transformations)

I found an excersice in Byron-Fuller's: "Mathematics of Classical and Quantum Physics", about the energy which is transferred to a spring by a time depended force of the form: $F(t)=\left\{ ...
-1
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1answer
42 views

Why can't you ride a bike with a fixed handlebar?

I tried one time, as part of an experiment, to ride a bike with a fixed handle bar. Impossible. So, in any case, our movements made with the handlebar helps us in not falling down. I can feel kinda ...
0
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4answers
261 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 & ...
1
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1answer
26 views

Why surface tension behaves so differently?

When a needle (or any other object) floats on water, its acting upwards balancing the gravity. But when an object (or may be a needle suspended in water) submerged in water, it acts downwards. ...
0
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0answers
30 views

How to find potential energy(PE) of a system in order to write Lagrangian? Is there is any unique way to write PE for different system?

for simple pendulum or spring system its very easy . we use mgl and mgh. What I need is the unique way which will help to write PE to all the systems.
0
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0answers
10 views

Piezoelectric slab (cantilever) with voltage

I am studying this specific piezoelectric slab with voltage applied The piezoelectric equation is $$ \left[ \begin{array}{c} \sigma_{1}\\ \sigma_{2}\\ \sigma_{3}\\ \sigma_{4}\\ \sigma_{5}\\ ...
3
votes
0answers
45 views

Physical Interpretation of the Graph of the Legendre Transform?

See Making Sense of the Legendre Transform and Legendre Transforms for Dummies. Look at the following diagram from the first link: I was trying to think of the simplest example to interpret this ...
0
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1answer
25 views

How does string tension influence the harmonic spectrum?

Hey there fellow physicists & musicians! I have a question both physics and music related. How does the string tension affect the sound spectrum? More precisely, how do the respective ...
6
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4answers
632 views

Does Dirac's argument against classical mechanics stand in contradiction to Bohm's theory?

In his book on Quantum Mechanics, P.A.M. Dirac talks about the stability of the atom as a means of demonstrating the need for quantum mechanics. He writes: The necessity for a departure from ...
0
votes
1answer
48 views

Velocity from the cumulative distribution function of the Boltzmann distribution

I want to get a Boltzmann distribution of the $v_x$, $v_y$ and $v_z$ velocity components (please, notice that the distribution is one-dimensional). To do so, I need the cumulative distribution ...
0
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2answers
37 views

Galilean invariance and the Lagrangian

My textbook says that in a time invariant space with translational and rotational symmetry the Lagrangian only depends on the magnitude of the velocity. The galilean invariance says that a Lagrangian ...
-1
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1answer
46 views

Force and energy relation: in case of time dependent force

The equivalent problems are also found in Marion problem 7-22, and other formal classical mechanics textbook. Here what i want to know why instructor solution and some websites gives this kinds of ...
1
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0answers
42 views

Which condition is stronger - ergodicity or mixing?

Reading a statistical physics book, I've encountered the following assertion (without further explanations): [..] the presence of dynamical instability makes the trajectory of a system much more ...
3
votes
1answer
39 views

Problem books for concept building in applications of Riemannian and other geometries to mechanics

As a student of physics I have learned solving Euler equations for rigid bodies by solving examples and exercises in self-contained books rather than understanding the proofs of Euler equations (I ...
1
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1answer
33 views

Finding the Mass of a Precessing Top

Consider a symmetric, non-nutating precessing top with one point fixed (the tip if you will). It's symmetry axis is at an angle $\theta$ to the vertical and it steadily precesses at some angular ...
1
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2answers
37 views

Rotation matrix for aligning x-axis in an arbitrary direction

I want to align the x-axis of my coordinate system, with an arbitrary direction in space $\hat{n}$. About which axis should I rotate? Ceratinty rotation about x-axis or $\hat{n}$-axis will not serve ...
4
votes
1answer
66 views

What is the specific source(s) of sliding kinetic friction

In simplistic (K-8) physics classes, it seems to be generally instructed that the friction between two moving surfaces is due to the unevenness of each surface and the microscopic roughness. However, ...
1
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1answer
116 views

Spherical phase space dynamics

I have a hamiltonian of the form $$H(\phi,z) = (1-z^2)\cos(2\phi) + \chi z^2$$ with position $\phi$ and conjugate momentum $z$. It has this form provided that $z \in [-1,1]$ and we have natural ...
25
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4answers
1k views

Does topology have any role in classical physics?

I've seen many applications of topology in Quantum Mechanics (topological insulators, quantum Hall effects, TQFT, etc.) Does any of these phenomena have anything in common? Is there any intuitive ...
0
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2answers
65 views

Average acceleration: why I am getting different results?

Let's consider a simple school problem. A car starts moving during 3 seconds with a constant acceleration of 1 m/s^2. Then it stops accelerating and moves 3 seconds more with a constant speed. Find ...
-1
votes
1answer
22 views

Change in Translation Kinetic Energy to Rotational Kinetic energy [closed]

A 56kg student runs at 5. 0 m/s, grabs a 10m hanging rope, and swings out over a lake. He releases the rope when his velocity is zero. What is the angle Q when he releases the rope? What is the ...
0
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0answers
16 views

Modelling point force with uncertain point of concentration [closed]

I consider a beam which is bent under influence of a point force concentrated at some point $\xi$ of the beam. The exact co-ordinate of $\xi$ is not known, but it is known a neighbourhood ...
-4
votes
1answer
60 views

What happens to gravitational potential when the mass disappears?

This is from a section of my website. Please tell me where it is wrong. Consider two stationary gaseous planets, both made entirely of deutrium. As the two planets are moved closer to each other ...
2
votes
2answers
339 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 ...
3
votes
1answer
41 views

Why does the 'Jacobian of at least one combination of $n$ functions shall be different from zero'?

I've started reading The Variational Principles of Mechanics by Cornelius Lanczos; here is the concerned excerpt from p. 11: The generalized coordinates $q_1,q_2,\ldots, q_n$ may or may not have a ...
3
votes
1answer
38 views

A pendulum attached to a spring and all the system is rotating with angular velocity

Find the all the constraints and a set of generalized coordinates A pendulum attached to a spring and all the system is rotating with angular velocity $\omega$. this is what I have done, I do not ...
0
votes
1answer
156 views

Consistent method for finding direction of static friction

I am having trouble coming up with a consistent method of determining the direction of static friction. So far the best I have come up with is: it should oppose the relative acceleration the contact ...
3
votes
3answers
760 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
3
votes
1answer
90 views

Lagrangian Equations of Motion, Conservative Forces

I'm new to this topic so please bear with me. Here on wikipedia we have the Lagrangian equations of motion: $$ \frac{d}{dt}\left(\frac{\partial T}{\partial \dot{q}}\right) - \frac{\partial ...
7
votes
0answers
113 views

How to properly use Perturbation Theory in classical systems?

Context: If we consider a particle in upwards motion near the Earth's surface and acted by a quadratic drag we get the non-linear eom: $$\frac{dv}{dt}=-g-\frac{b}{m}v^2.$$ We can solve it ...
0
votes
0answers
23 views

Two axis non linear Inverted Pendulum

I am Electronic Engineering student. Sorry for my english, I am very rusted. I am modeling the inverted pendulum for a Class Project and I wondering if any could answer one question. In this web ...
0
votes
2answers
32 views

How to prove that the potential of a conservative central force depends only on the magnitude of the distance & not on the direction of the vector?

If a conservative central force acts on a body then its potential only depends on the magnitude of the distance between two bodies (does not depend on direction of vector). Is there any proof of it ...
0
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0answers
23 views

Are time-$t$ maps of a Hamiltonian system with 1 degree of freedom typically twist?

If we take a typical Hamiltonian system $H(q,p)$ with one degree of freedom, and look at its time-$1$ map $(q(0),p(0)) \mapsto (q(t),p(t))$, will it generically satisfy the twist property, e.g. ...
46
votes
6answers
5k views

Why does a system try to minimize its total energy?

Why does a system like to minimize its total energy? For example, the total energy of a $H_2$ molecule is smaller than the that of two two isolated hydrogen atoms and that is why two $H$ atoms tries ...
6
votes
2answers
1k views

What is the highest energy position for a double pendulum? And for which energy positions is it chaotic?

Math/physics teachers love to break out the double pendulum as an example of chaotic motion that is very sensitive to initial conditions. I have some questions about specific properties: For a ...
1
vote
2answers
55 views

Is there any general theorem which specifies conditions where the critical solution of an action is unique (for given boundary conditions)? [duplicate]

Consider a classical mechanical system with generalized coordinates $q_i$, $i \in \{1,\dots\,n\}$. And Lagrangian $L$. Given a path $\gamma$ (with coordinates $\gamma_i$) and two times $t_1$ and $t_2$ ...
0
votes
0answers
90 views

Uniformly/proportionally banking a rolling torus regardless of it's spinning speed [closed]

TL;DR I am working on a video game. Torus rolls down the hill. I want to make it turn. Instead of rotating it towards the expected direction, I am looking to bank it. Superbike idea, with just one ...
1
vote
1answer
315 views

What are the mathematical models for force, acceleration and velocity?

In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
1
vote
2answers
48 views

Difference between inviscid and viscous flow

In my lecture notes, I have a load of examples and I want to sort out which egs are viscous flow and which are inviscid flow. It is not always said if the flow is viscous or inviscid. Please can ...
1
vote
0answers
36 views

Photon transmission

I want to know exactly how light travels. Are each photon in a light beam traveling in a cosine function? I'm confused because only when it goes through polarization that it starts to show this type ...
0
votes
1answer
33 views

Viscous fluid boundary condition

Consider an incompressible viscous fluid of kinematic viscosity $ν$ , dynamic viscosity $µ$ and density $ρ$ . A viscous boundary layer is located over a solid surface at $y = 0$ and $x > 0$. The flow ...
1
vote
5answers
124 views

Airplane on a treadmill - Variant Thought Experiment

This thought experiment is in a way related to the (in)famous airplane on a treadmill problem. If you take a ball and place it on a treadmill, will the ball: Move backwards relative to the ground ...
3
votes
1answer
205 views

Marvin the Martian vs. the Death Star: how much energy will they actually need to disintegrate the Earth?

According to a detailed analysis by Dave Typinski, Marvin the Martian’s Illudium Q-36 Explosive Space Modulator will require $1.711 \cdot 10^{32}~\text{J}$ to shatter the Earth into a gravitationally ...
10
votes
6answers
2k views

Why is a beam reach the fastest point of sail on modern sailboats?

I've heard that a beam reach (perpendicular to the wind) is the fastest point of sail on modern sailboats, but I haven't heard a satisfying explanation of the physics behind the claim. Triangular ...
1
vote
1answer
63 views

Normal reaction [closed]

Consider a plank on a frictionless surface and a ball from a height H is dropped on this plank. There is no friction between the plank and ball. Can the plank jump up in air for any value of H? I ...
1
vote
1answer
34 views

Finding boundary condition of stationary solid body

A fluid flows past a stationary solid body of arbitrary shape. Write down the boundary condition on the fluid velocity $\textbf u$ for an inviscid fluid and for a viscous fluid, at the solid surface. We ...