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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Why fall bombs always in a horizontal position?

I´m not sure but it seems to me when bombs are dropped they always fall in a horizontal position. Which is to say, not with their nose down. What´s the reason for this?
2
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2answers
88 views

Validity of the Lyapunov exponent approximation

I was trying to get the Lyapunov exponent for some dynamical nonlinear systems and found that it is not true (as I had expected) that the distance between two trajectories with slightly different ...
0
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1answer
31 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
52 views

Classical dynamics of a matrix

For a system of interacting particles, we can formulate Hamiltonian dynamics in terms of a vector of position coordinates $q$ and a vector of momentum coordinates $p$. Then the Hamiltonian takes the ...
1
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1answer
37 views

Why does time-independent Hamiltonian not depend on angle variable?

In Landau and Lifshitz Mechanics, $\S50$ Canonical variables a time-independent Hamiltonian is considered, and a canonical transformation is done such that adiabatic invariant $I$ becomes the new ...
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2answers
154 views

Infinite pulley system

http://www.physics.harvard.edu/uploads/files/undergrad/probweek/sol43.pdf Hi, I've been trying to solve this question for a while, I understand the first solution and also the solution to the second ...
3
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2answers
168 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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0answers
24 views

Calculate the ‎displacement and velocity after 4 seconds and calculate the maximum displacement and velocity [on hold]

The shown frame is subjected to initial displacement 10 cm at the floor level. Calculate the ‎displacement and velocity after 4 seconds and calculate the maximum displacement and velocity. ‎The story ...
16
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3answers
336 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. ...
2
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5answers
370 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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1answer
62 views

Springs, elastic potential energy, kinetic energy

If a ball with some kinetic energy collides with a spring, the ball doesn't lose its kinetic energy in an instant, right? it loses kinetic energy as the spring gains potential elastic energy. Right? ...
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0answers
23 views

The geometrical-locus result of collision and fall

A classical momentum-conservation experiment follows about this way: On a table there is a sloped track and a ball is rolled down. At the bottom of the track, a second ball is at rest. The balls ...
1
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2answers
50 views

How do I find the linear components of acceleration in a pendulum?

I have managed to derive the equation of motion of a simple pendulum under the influence of gravity using the Lagrangian, but since that only tells me what the angular acceleration is, I now want to ...
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1answer
61 views

Why is angular acceleration of a pendulum always negative?

I was trying to derive using the Lagrangian the equations of motion of a simple pendulum under the influence of gravity. Eventually, I was brought to this conclusion: $$\alpha = -(g\sinθ)/l$$ where ...
17
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1answer
613 views

Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
2
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1answer
299 views

Hyper/parabolic kepler orbits and “mean anomaly”

In an elliptical kepler orbit there is an easy recipe to describe the motion/position of a satellite at time $t$. One just follows the following steps - an important detail for me is that the ...
8
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4answers
714 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 ...
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0answers
41 views

Derivative of an integral help [closed]

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
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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
41 views

Determining the Lagrangian of a double pendulum [closed]

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 ...
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1answer
45 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 & ...
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1answer
32 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. ...
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0answers
33 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.
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0answers
11 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
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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 ...
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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 ...
0
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1answer
51 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
38 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 ...
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1answer
49 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 ...
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0answers
45 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
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1answer
40 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
34 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
38 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
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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
117 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
71 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 ...
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1answer
61 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
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2answers
340 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
46 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
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1answer
39 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
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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
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1answer
91 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 ...
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0answers
114 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
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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 ...
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2answers
33 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 ...
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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. ...
47
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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 ...