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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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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32 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 ...
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2answers
64 views

Where does energy go when performing a useless effort?

I went to school one day, so I thought I was able to get this simple one.. but it looks like I'm not anymore. :( One lonely little spaceship is resting into space. It has a small fuel capacity that ...
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1answer
17 views

How do I calculate motor efficiency from voltage, current and RPM?

I have a setup where a motor is spinning at a constant (known) RPM, under no load. I know the power going into the motor (voltage * current), and I can find out the rotational kinetic energy of the ...
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1answer
31 views

Why the involution condition is imposed in the definition of integrability?

For an $N$-degree-of-freedom system to be integrable, the usual definition imposes the existence of $N$ independent conserved quantities, which must be in involution to each other, i.e., $$\{ F_i, ...
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48 views

Landau's derivation of a free particle's kinetic energy- expansion of a function?

I was reading a bit of Landau and Lifshitz's Mechanics the other day and ran into the following part, where the authors are about to derive the kinetic energy of a free particle. They use the fact ...
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53 views

Sufficient conditions for the energy to be not conserved?

I'm almost embarrased to ask this question because I thought I was by now very confident with classical mechanics. Someone has stated that given a mechanical system with a Lagrangian $L$ s.t. ...
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2answers
61 views

Could two identical stars revolve around each other in a common orbit if we only account for Newtonian physics?

Both a parent star and its planet revolve around the center of mass of the system, the reason we see stellar wobble. But if we take this to be true, which it is, there can be a configuration in which ...
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48 views

About the derivation of the Hamilton-Jacobi equation

It is an old question for me. In Goldstein's book, the H-J equation is derived in this way. We want to find a generating function $F(q,P,t)$ such that the transformed Hamiltonian vanishes identically, ...
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45 views

Dimension agreement in canonical transformation

In this Physics.SE post, there is a transformation: $$Q = q,$$ $$P = \sqrt{p} - \sqrt{q}.$$ for Hamiltonian $H = \frac{p^2}{2}$. The post discusses the validity of this transformation as a canonical ...
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1answer
15 views

Resonance of a tube of air in case of more complex shapes

I've been thinking about posting this question on Music Performance stack, but finally I think it fits more here since I'm interrested in technical details. The subject of resonance of a tube of air ...
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1answer
39 views

Can all canonical transformation be obtained through generation function approaches?

The question can be formulated as following: Suppose $$\delta \int_{t_1}^{t_2}{[p\cdot \dot{q} - H(p,q,t) ]dt} = 0$$ $$\delta \int_{t_1}^{t_2}{[P\cdot \dot{Q} - K(P,Q,t) ]dt} = 0$$ in which $$P = ...
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1answer
54 views

Is static friction an impulsive force?

For example: let's consider a static sphere on an horizontal rough surface. I apply an impulse $J$ parallel to the ground and in the middle of the sphere. If, like my book says, the friction is not an ...
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2answers
56 views

Sea surfer position displacement

Waves are means by which the energy propagates through a medium (e.g., sea water). This is not associated with a net movement of water in the direction of wave propagation. If this is the case, then ...
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1answer
31 views

Planar motion in central forces

In a two body problem under central force, corresponding to a potential $V(r)$(assume one body is massive compared to the other so that its motion is negligible), conservation of angular momentum ...
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2answers
88 views

Action and Action integral: Different kinds of variational principles

What are the difference between: the action $\int_{t_{1}}^{t_{2}}(L+H) dt$ that we use in the principle of least action, and the action integral $\int_{t_{1}}^{t_{2}}L dt$ that we use in ...
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59 views

Invariance of canonical Hamiltonian equation when adding the total time derivative of a function of $q_i$ and $t$ to the Lagrangian

The following is exercise 8.2 in 3rd edition (and exercise 8.19 in 2nd edition) of Goldstein's Classical Mechanics. Adding the total time derivative of a function of $q_i$ and t to the Lagrangian ...
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3answers
74 views

Is thermodynamic free energy and potential energy the same thing?

The equation for free energy $F$ and potential energy $E_{pot}$ are: $$ F=U-TS \\ E_{pot} = E_{tot} -E_{kin} $$ But the temperature $T$ is proportional to the average kinetic energy of a system. So ...
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1answer
41 views

Physics of Snow Globe

What is the physics behind snow flakes inside a 3D snow globe? If I were to implement a snow globe in computer graphics what kind of model do I need to the flakes motion like a real snow globe? What ...
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1answer
66 views

How to prove that a hamiltonian system is not integrable?

To show that a system is integrable, we just need to find $N$ independent functions $f_j$ such that $\{ f_i, f_j \} = 0$. But how to prove that such a set of functions do not exist? For example, ...
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73 views

Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
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Is there a physical system whose phase space is the torus?

NOTE. This is not a question about mathematics and in particular it's not a question about whether one can endow the torus with a symplectic structure. In an answer to the question What kind of ...
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152 views

When is this integral zero?

I have a particle with total energy $E$ confined in a potential $$U(x) = -\frac{\cos^4x}{2} - m \cos x - f \sin x. $$ The constants $f$ and $m$ are both in the range (-2,2). The energy is such that ...
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45 views

Are there any hamiltonian systems without a periodic orbit?

Are there any hamiltonian systems without a periodic orbit? Can anyone give me an example? If such a system exists, does this fact have any implication on its quantum version?
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103 views

I am learning Quantum Mechanics and I have some questions about some basic concept [closed]

What does a "STATE" exactly mean in quantum mechanics? What is the equivalence of "STATE" in classical mechanics? If we have a wave function $\Psi$ , its absolute square $|\Psi|^2$ is the ...
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2answers
78 views

Electrical force between two objects

I tried to solve the following problem: There are 2 objects . The object m1 with charge q and the object m2 with charge q.(same charge).The object m2 is connected with a rope to the ceiling. at the ...
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2answers
109 views

Antipodes are mostly ocean - so what happens after digging that hole through earth?

Digging a hole through earth is a common thought experiment, often used to explain effects of gravity. But what would happen if someone finally dug the hole? Sure, he took care to stabilize and ...
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2answers
104 views

What's wrong with my calculation of gravitational potential for a uniform sphere?

This is really embarrassing, but I'm not quite sure where I'm going wrong here... Why is this calculation of the gravitational potential inside a sphere with uniform mass distribution incorrect? ...
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1answer
150 views

Classical vs. quantum energy of the hydrogen atom

If I have an electron and a proton and calculate the classical energy which I get by bringing the electron from infinity to the distance of a Bohr radius to the proton, I get 27.2 eV, but the electron ...
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1answer
109 views

Does a simple double pendulum have transients?

Suppose, we have the most simple double pendulum: Both masses are equal. Both limbs are equal. No friction. No driver. Arbitrary initial conditions (no restriction to low energies) Does this ...
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0answers
64 views

Naive questions on the classical equations of motion from the Chern-Simons Lagrangian

Consider a Chern-Simons Lagrangian $\mathscr{L}=\mathbf{e}^2-b^2+g\epsilon^{\mu \nu \lambda} a_\mu\partial _\nu a_\lambda$ in 2+1 dimensions, where the 'electromagnetic' fields are $e_i=\partial ...
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35 views

How do adhesive and cohesive forces affect surface tension? [closed]

Surface tension appears at the interface of two immiscible fluids if the cohesive force of attraction is more than adhesive force. What will be the physical effect if the adhesive force is more than ...
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127 views

In what limit do we *really* get Maxwell-Boltzmann statistics from Bose-Einstein and Fermi-Dirac?

Fermi-Dirac and Bose-Einstein energy occupation number $n(\epsilon)$ in natural units ($[T]=[\epsilon]$) read $$n(\epsilon) = \frac{D(\epsilon)}{e^{(\epsilon-\mu)/T}\pm 1},$$ where $D(\epsilon)$ is ...
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CM: Need to recover the Hamiltonian, knowing conserved quantities and information about the EOM, possibly via action-angle coordinates

Statement of the problem: I have a system with 2 degrees of freedom and I have found two independent conserved quantities, without knowledge of the Hamiltonian. I'm looking for a method to recover a ...
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1answer
46 views

From 1D problem to easier 2D problem

Here I describe an example how a 1D problem can be solved easier by considering a mathematically equivalent problem in 2D. Problem: Find the equation of motion of particle in 1D space with the ...
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1answer
65 views

Kinetic energy in Lagrangian formalism

In reading Goldstein's Classical Mechanics (2nd edition) I came across a confusing derivation. Goldstein (Eq. 1-71) derives the total kinetic energy of a system of (classical) particles as: $$ T = ...
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0answers
35 views

How coordinate system shifting is related to similarity transformations?

I know that coordinate system shifting can be represented using matrices. But how exactly are similarity transformations related to coordinate shifts ?
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2answers
170 views

How should I throttle my rocket to reach highest altitude? [closed]

"Real world" problem. Suppose we want to launch a rocket equipped with an engine which can be throttled as we prefer. Suppose also that the amount of fuel burnt per time is directly proportional ...
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4answers
72 views

Basic buoyancy question

If I have a cup of water filled with air at the bottom of a pool, then when the cup is "upside down" the air doesn't leave because the water pressure is pushing it up against the top of the container. ...
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25 views

Block on an inclined plane [closed]

If you take moments about the centre of mass of a block positioned on an inclined plane so that the gravitational force can be drawn from the centre of mass of the block to one corner of the block, ...
4
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2answers
61 views

How much does the sound definition vary during an LP (Vinyl)?

This question came to me when I realized how the linear speed varies while listening to a Vinyl LP. The linear speed variation has to be compensated with a variation in the resolution of the grooves, ...
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3answers
231 views

Confusion regarding the principle of least action in Landau's “The Classical Theory of Fields”

Edit: The previous title didn't really ask the same thing as the question (sorry about that), so I've changed it. To clarify, I understand that the action isn't always a minimum. My questions are in ...
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28 views

Why and how almost periodic series constitute the algebra of observable of integrable systems?

In the introduction of his book Noncommutative Geometry, p. 42, Connes explains that when a classical dynamical system has enough constants of motions, the motion of the system is almost periodic, ...
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159 views

The boundary for quantum mechanical behavior and classical mechanical behavior

To what size and how does "quantum weirdness" such as entanglement and superposition stop applying to larger objects (mere unions of these quantum particles). How do these macro objects that behave as ...
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1answer
41 views

(air pressure and displacement) Isn't this image wrong?

Isn't this figure wrong? P(x,t) = -B(dy/dx) . If the derivative of air displacement has a maximum, then this is where the pressure is minimum, not maximum as this figure suggests. Could someone ...
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49 views

Types of invariance and their definitions

In classical mechanics, there are three types of invariance: invariance, form invariance and gauge invariance. I am looking for a precise definition of these terms, but all I can find are sentences ...
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260 views

Quantum Mechanics or Classical Mechanics? [closed]

I'm just a student of grade 11 but, I was interested in knowing about Physics much deeper. In order to start my interest in Physics, I watched this video of Quantum Physics NOVA : Quantum ...
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1answer
44 views

Sign of gravitational force

I'm reading Lanczos's The variational principles of mechanics, and on pp. 80-81 there is an example involving a system made up of $n$ rigid bars, freely jointed at their end points, and the two free ...
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3answers
162 views

Is escape velocity the same for all objects?

Would a lighter-than-air craft in the mid atmosphere at 80,000 feet altitude need to achieve the same velocity to escape earth gravity as the space shuttle?
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1answer
50 views

Standing wave velocity

My question is simple: How is it that a standing wave has velocity? I mean, it's not travelling... A lot of equations depend on this concept, for example: $f_n = \frac{nv}{2L}$ Here we're ...