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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Is temperature affected by gravitational potential?

Ok, I feel a bit silly asking this. I'm asking in relation to this question here on the molecular basis of hydrostatic pressure in a gas. There's been quite a bit of discussion and one of the ...
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50 views

Canonical transformation from Hamiltonian without external source to Hamiltonian with external source

Let a system with time-independent Hamiltonian, $H_0(q,p)$ be subjected to an external oscillating field $E_0\sin(wt)$, so that the Hamiltonian becomes $H=H_0(q,p)-qE_0\sin(wt)$. Find a canonical ...
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1answer
59 views

Lagrangian under time transformation

Given a Lagrangian $$L(q,\dot{q},t)=\sum_{ij}a_{ij}(q)\dot{q}_i\dot{q}_j-V(q_1,q_2,\cdots,q_f)$$show that under a time transformation $t=\lambda T$ ($\lambda$ = constant), the invariance of ...
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2answers
55 views

Conservation of energy when the Lagrangian includes a potential function

When proving that the homogeneity of time leads to the conservation of energy, (This is the proof from Landau for the case when there is no field present.) (Uses the Einstein's summation ...
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165 views

Trouble with Landau & Lifshitz

Hello I have a quick question on what I have been reading in Landau & Lifshitz's book on classical mechanics. I am in the very beginning of the book and I am having trouble with his derivation on ...
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1answer
48 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 ...
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35 views

How do I prove that frequencies that are irrationally related lead to quasi-periodic motion?

Consider the equation: \begin{equation} \dot{x} = Mx, \end{equation} where \begin{equation} M = \begin{pmatrix} i\omega_1 & 0 & \cdots & 0 \\ 0 & i\omega_2 & \cdots & 0 \\ ...
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1answer
66 views

Time reversal in simple *solution* to equation of motion

Consider the solution to the equation of motion for a particle with a constant acceleration: $$ x(t) = x_0 + v_0t + \frac{1}{2}at^2.$$ If I let $t \rightarrow -t$, then the equation becomes: $$ x(-t) ...
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1answer
47 views

Direction of velocity confusion on inclined plane

In Taylor's book Classical Mechanics, pg. 259, he works through the following example: Consider the following block and wedge system: The block ($m$) is free to slide on the wedge and the wedge (mass ...
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1answer
122 views

How does temperature in a solid sphere change with time when moving through a gas?

I'm interested in the following problem: There is a solid sphere with radius $r$ and mass $m$ at temperature $T_{s0}$. It is moving at velocity $v_s$ through a gas of temperature $T_g$. How does the ...
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1answer
48 views

Will the bouncing particle exert greater force on the surface?

Imagine elastic collision and no energy is lost from the system. A particle is emitted from the bottom of a box. The box is in inertial motion. The particle hits the top of the box and travels in ...
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1answer
75 views

Transfer between translative KE and rotational KE in a rigid body

I have been inspired by some sci-fi cannons that seem to operate by initially spinning up a projectile inside the cannon, and then suddenly firing the projectile out at high speed. Now, I am wondering ...
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1answer
61 views

Star vibration frequency due to gravitation

I found the following problem on a Classical Mechanics MIT problem set, which is intended to be solved by dimensional analysis: Derive an expression for the vibration frequency of a star of mass M ...
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0answers
75 views

Normal Modes of a Suspended Rod with Strings of Fixed Lengths [closed]

A thin uniform rod of length $ 2b $ is suspended by two vertical light strings, both of fixed length $ l $ , fastened to the ceiling. Assuming only small displacements from equilibrium, find the ...
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1answer
39 views

If $(q,p)$ to $(Q,P)$ is a canonical transformation, then does this imply $(Q,P)$ to $(q,p)$ is also?

If $(q,p)$ to $(Q,P)$ is a canonical transformation, then does this imply $(Q,P)$ to $(q,p)$ is also, assuming Hamilton's equations hold for the coordinates $(q,p)$? This seems like it should be true ...
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5answers
444 views

How do I turn my bicycle?

No doubt a very simple question with an easy answer that's been puzzling me: If I'm riding my bicycle in the $x$ direction with speed $v$ and turn my handlebars I can end up travelling in the $y$ ...
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0answers
21 views

Impact strength test of a container filled with liquid

as a university project I have to project(choose material and dimensioning) a liquid container (NaClO, density 1100 g/L), we ...
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1answer
57 views

Work done: kinetic energy or area under F-ds curve?

Starting from $$F=ma = m \frac{dv}{dt} = m \frac{ds}{dt} \frac{dv}{ds} = m v \frac{dv}{ds}, $$ leads to work done = integral of F.ds = integral of mvdv = change in KE. Suppose a variable force is ...
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1answer
93 views

Is it possible to write explicitly the exact solution for forced damped harmonic oscillator?

Preamble Consider a damped harmonic oscillator, with his well know differential equation \begin{equation*} m \ddot{x} + c \dot{x} + kx=0 \end{equation*} and let's find the solution that satisfies ...
2
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0answers
45 views

Where does the Lagrangian come from? [duplicate]

It always puzzles me whenever I work on Lagrangian equations. It is easy to see that $L=T-V$ yields the correct equations of motion, but the question is, how do you get to that formula? Is it trial ...
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1answer
66 views

Determining the geometry of the phase space of a system [closed]

How do we check the geometry of the phase space ? I mean in classical mechanics we use position and conjugate momenta as a space of all possible states of the particle. How do we know that this phase ...
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0answers
8 views

solve r2 and r3 [closed]

i am working through a balancing of machines question. i cannot figure out how in the text book they get the RHS to equal 16.538 and 10.4045. i think everything needed is included in the photos. if ...
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2answers
58 views

What is the initial angular momentum of a rigid body given an offset impulsed force?

What is the imparted angular momentum to a rigid body if the impulse force is offset by a distance $h$ from the center of mass and the imparted momentum from the center of mass is $mv$? For a ...
2
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1answer
49 views

Reversibility in classical mechanics

I am watching Susskind's 'Theoretical Minimum' videos. At one point in his course on classical mechanics (2nd video if I remember correctly) he affirms that Netwon's second law of motion makes ...
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4answers
86 views

Is trajectory the same as an orbit?

Is trajectory the same as an orbit? I wanted to know about gravity assists, but most books I find are talking about different types of orbits and such. Are they related?
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1answer
124 views

Maths behind gravity assist

What kind of maths is behind gravity assists and in general the theory of orbits, and how deep does it go? I am just wondering if I know enough prerequisites!
3
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1answer
77 views

How do I transform onto a relativistic rotating frame of reference?

In classical mechanics, the usual formula to translate the evolution of a quantity as seen from an inertial frame of reference to a rotational frame is: $$\frac{d \textbf{A} }{dt} \vert_{Inertial} = ...
3
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2answers
131 views

What's the true reason behind thermal expansion?

Thermal expansion is a normal concept everyday. There are 2 explanations: 1, thermal expansion result in stress, then result in deformation 2, thermal expansion result in deformation, then result in ...
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5answers
125 views

Why are position and velocity enough for prediction and acceleration is unnecessary?

In classical mechanics, if you take a snapshot and get the momentary positions and velocities of all particles in a system, you can derive all past and future paths of the particles. It doesn't seem ...
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1answer
79 views

Coupled wheel and rod (analytical mechanics)

I am struggling with formulating the equations of motion. Consider a coordinate system with origin in $O$ ($y$ upwards and $x$ to the right), label the center of mass of rod $AB$ with $G$ then: ...
2
votes
1answer
77 views

Measuring the pressure in a container without changing it [closed]

Let's say I have a closed, non-transparent metal container with pressurized gas and I'd like to measure the pressure inside without changing that pressure (or changing it as little as possible). The ...
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2answers
100 views

How to reconstruct the dependence of the potential from a coordinate?

What is known is that an ion sent along the X-axis of a black box with a speed $V$ returns in a time: $$T=a V^b$$ $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of ...
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10answers
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In reverse time, do objects at rest fall upwards?

I want to develop a game where time runs backwards, based on the idea that physical laws are reversible in time. However, when I have objects at rest on the earth, having gravity run backwards would ...
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1answer
70 views

How do you find the tension in the real world? (Given a rope in a pulley system)

I'm well aware of the formula to calculate tension, however, given a real world situation where you have a closed pulley system. How do you measure the force (i.e., tension) required to pull on the ...
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2answers
126 views

Force needed to push a syringe plunger: does one add force associated with downstream back-pressure to frictional plunger force?

I am trying to figure out how much force $F$ is needed to push a syringe plunger. The plunger needs to overcome the friction force $F_1$ and (a much smaller) inertia force $F_2=ma$, giving the total ...
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0answers
49 views

Are there limits to human/devices perception?

As far as i know, measurement devices present measurements based on something that affects the device's particles, for instance, forces, heat, tension, voltage... My question is, given that every ...
5
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3answers
144 views

How do we know that the Fourier transform of space is momentum?

How do we know that the Fourier transform of real space $x$ is the momentum $p$ space or for energy and time, receptively? What's the mathematical process and physical logic?
0
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1answer
71 views

spinning a water bottle quickly

When we spin a water bottle so quickly, why don't the water inside the bottle come out ? It has to do with the normal force and the apparent weight , i think . but plz someone explain for me how does ...
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0answers
37 views

Describing the motion of a point-mass [closed]

Consider a point-mass moving around a fixed point on a circle with radius $r$ with constant angular velocity $\omega$. At a certain moment of time, the connection is removed, and the point-mass flies ...
1
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1answer
32 views

Simulating Phase Space Evolution

I am interested in modeling the time evolution of phase-space $\rho(\vec{q},\vec{p},t)$. I have attempted to use Liouville's theorem $\partial_t\rho=-\sum_{i=1}^{3}(\partial_{q_i}\rho)\dot ...
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0answers
26 views

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

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 ...
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0answers
130 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 ...
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2answers
144 views

What's the physical interpretation of an arbitrary normal mode for masses and springs?

Consider the following system consisting of 3 masses and 4 springs : I have learned that this system posseses three normal modes, corresponding to its three natural frequencies, say ...
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5answers
842 views

Classical Mechanics contradicts Conservation of energy?

Imagine a Stanford torus rotating with 1 rpm so that centripetal/reactive centrifugal acceleration provides about 1.0g of artificial gravitational acceleration inside the ring. The picture below shows ...
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1answer
42 views

What am i doing wrong here(dynamics)?they should give the same answer [closed]

So a body $m$ is on a uniform circular motion ($\omega = d\theta/dt = \text{constant}$), it is suspended by an inextensible rope with negligeable mass: First picture so: $$ -mg + T \cos \alpha = ...
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1answer
109 views

Is there an error in Susskinds' derivation of Euler-Lagrange equations?

http://imgur.com/kZO5C0V First, I believe there is a trivial error. The second equation should have another $\Delta t$ multiplying everything on the right. It is divided out later when the equation ...
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46 views

Equilibrium Points in Lagrangian Mechanics

Suppose we have a one particle system with generalized coordinates $q_i$. In classical mechanics, the corresponding Lagrangian is $L = T - V$. Assume $V(q)$ is time-independent. What additional ...
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1answer
26 views

Period of swinging incomplete hula-hoop

I was working on a problem where I had to calculate the period of a swinging incomplete hula-hoop given its center of mass and radius. It only swings with very small amplitude so I considered the ...
2
votes
1answer
65 views

Does Special Relativity require a “ruler postulate” analogous to the “clock postulate”?

It's fairly well known that the clock postulate is needed in Special Relativity when dealing with accelerated clocks, so does something analogous exist when dealing with accelerated spatial ...
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1answer
91 views

Analytical Mechanics [closed]

This is one of my three homeworks. I see that $W_a(1) = \dot U_a(1)=\ddot{X_a}(1) = 0.3 $ Since $U_{O'}=0 $ then O' is Instant centre of rotation. Then $U_b = 2U_a = 0.6$ I tried a lot, about a ...