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Questions tagged [classical-mechanics]

Classical mechanics discusses the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces). If it's possible, USE MORE SPECIFIC TAGS like [newtonian-mechanics], [lagrangian-formalism], and [hamiltonian-formalism].

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Connection between dispersion relation and symmetries of the Hamiltonian

I am having trouble understanding intuitively the connection between the dispersion relation and the symmetries of the Hamiltonian. For example, suppose we have a lattice and there are four sub-...
JosephSanders's user avatar
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Does electric and magnetic field from electromagnetic radiation are 2D based? [closed]

I'm getting into physics, specially in electromagnetism. When we're talking about electromagnetic radiation. Does it has a 2D shape when it's propagating through space? Does Maxwell's equations ...
Psi's user avatar
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Strogatz's condition on definition of energy

In, Nonlinear Dynamics And Chaos, 2nd edition page 160, by Steven H. Strogatz, he writes Let’s be a bit more general and precise. Given a system $$\dot x =f(x),$$ a conserved quantity is a real-...
GedankenExperimentalist's user avatar
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What is the relationship between phase space and Jacobian in Nakahara Eq.1.15 (under this equation)?

In Nakahara's Geometry, topology and physics, under Eq.1.15 they give an equation \begin{align*} \det\left(\frac{\partial p_i}{\partial\dot{q}_j}\right)=\det\left(\frac{\partial^2L}{\partial\dot{q}_i\...
liZ's user avatar
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3 votes
1 answer
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Does quasi-symmetry preserve the solution of the equation of motion?

In some field theory textbooks, such as the CFT Yellow Book (P40), the authors claim that a theory has a certain symmetry, which means that the action of the theory does not change under the symmetry ...
Hezaraki 's user avatar
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1 answer
25 views

Work Done by kinetic friction in Circular Motion

We know when an object is moving in a circular motion on a rough horizontal surface, direction of kinetic friction is constantly. Thus, fto calculate the work doen by friction, we need to use ...
Akhilesh G's user avatar
5 votes
5 answers
774 views

How can I interpret the normal modes of this mechanical system?

How can I interpret the normal modes of this mechanical system? The equations of motion for the system are as follows: $$\left[\begin{array}{ccc} m_{1}\\ & m_{2}\\ & & 0 \end{array}\...
fortega20's user avatar
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0 answers
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Determining Equivalent Point Forces for a Rigid Body Given Net Force and Torque [closed]

Consider a rigid planar body subject to a force field, such as the gravitational interaction between polygons in a 3D space described in this question. Given: The net force acting on the rigid body ...
user1420303's user avatar
7 votes
4 answers
573 views

Does a rocket moving in a circle expel exhaust at a greater velocity?

Consider a rocket undergoing constant acceleration in a rectilinear path. Assuming the rocket is ideal (ignoring fuel mass and energy loss such as sound, radiation, vibration, etc.) a portion of the ...
Trever Thompson's user avatar
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2 answers
81 views
+50

Doppler shift from a moving reflector and source if only the relative velocity is known?

Suppose there is a device which is producing and listening to sound (sonar), a reflector is moving with respect to device and the velocity of reflector and device with respect to the air is not known, ...
Pradyuman's user avatar
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How does total cross section converge? [closed]

I am reading Statistical Mechanics by Reif, and when discussing collisions he brings up the notion of cross sections. He defines it by $d\mathcal{H}=F\sigma \mathrm{d}\Omega$, where $\mathcal{H}$ ($\...
user62783's user avatar
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In the flow equation in Lecture 9 from Susskind’s ‘Classical Mechanics’, why is there a negative sign? Why is there partial and regular derivatives?

Lecture 9 of Susskind’s ‘Classical Mechanics’ has a section titled ‘Flow and Divergence’ (pages 165-167). The section discusses flow in a box with side lengths $dx$, $dy$ and $dz$. He says that if the ...
Bradley Peacock's user avatar
3 votes
2 answers
620 views

Areas with anti-parallel gravity in classical physics

I cannot indicate an error in the following reasoning if it is done in the framework of classical physics. Let's make the imaginary setup with two wedges and the ball, when the gravity in the left ...
Artem's user avatar
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2 answers
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Equilibrium in physics

We know that harmonic oscillator or pendulum will not reach a equilibrium at infinite time. But why a system of gas molecules reaches equilibrium (entropy of an isolated system will tend to increase ...
Mantu Das's user avatar
3 votes
0 answers
58 views

Are Landau-Lifshitz equations equivalent to Hamilton's equations for classical spins?

Let $\boldsymbol{s}_1$ describe a "classical spin", i.e. a point on the surface of a unit sphere embedded in $\mathbb{R}^3$. It can be parametrized, for example, as $$ \boldsymbol{s}_1 = \...
QuantumBrick's user avatar
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0 answers
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I need an explanation for the time derivative omissions when solving for the Lagrangian of a system [closed]

So I have been self-studying Landau and Lifshitz’s Mechanics for a little bit now, and I have been working through the problems, but Problem 3 is giving me some trouble. I solved the Lagrangian ...
Justyn's user avatar
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3 answers
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Question regarding gravitational force as external force

So, I was watching a lecture on YouTube for problems on conservation of energy and momentum and I don't quite understand this: In this question, mass $M$ is released from the peak of the smooth ...
Hrishikesh Pandey's user avatar
-3 votes
0 answers
32 views

I am trying to derive an expression for the magnetic field of charged particles travelling at significant fractions of speed of light [closed]

I tried using lorentz transformation , which gives me correct answer for speed of light c but when i try to input any other values nearby c it becomes a constant B = 10-7 . q/r² ( (v - u)/ 1- uv/c²)
PhysicsEnjoyer31415's user avatar
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Justifying that the gold nucleus is at rest in a Rutherford experiment

This is an example on the Rutherford Experiment from Young and Freedman's University Physics. In the last paragraph of the solution the book states that it is valid to assume that the gold nucleus ...
nomadicmathematician's user avatar
5 votes
1 answer
625 views

Is it possible to understand in simple terms what a Symplectic Structure is?

I would like to understand what a Symplectic Structure is, and its implications in Classical Mechanics (Phase Space), but in pre-grade terms (If that could be possible). I have not taken any ...
L. G. Romero's user avatar
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0 answers
26 views

Diffusive momentum transport as overlap of acoustic peaks?

In the context of molecular dynamics simulations of soft or hard spheres in the fluid phase (e.g., with Lennard-Jones interactions), it is known that the velocity autocorrelation function (VACF) ...
YoussefMabrouk's user avatar
1 vote
2 answers
79 views

Massless String Having Different Tensions

I'm a student fairly new to physics, and I was working through a textbook (this is not for homework) when I came across a problem involving Two masses, $m$ and $2m$, hang over a pulley with mass $m$ ...
John Doe 's user avatar
-1 votes
0 answers
40 views

Getting an opposite sign for the centrifugal potential energy in the effective potential [duplicate]

Consider a system whose Lagrangian is $$L = \frac12 \mu\left( \dot r^2 + r^2 \dot\theta^2 \right) -U(r) $$ By the Euler-Lagrange equation, $$\frac{\partial L}{\partial\theta}=\frac{d}{dt}\frac{\...
xiver77's user avatar
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1 vote
2 answers
83 views

Understanding the “source” of magnetic energy in a bar magnet

I’m an amateur trying to grapple around this problem of what sources the magnetic energy in a bar magnet… We know that the source of the magnetic force that a bar magnet exerts is due to its magnetic ...
Vivek Kumar's user avatar
-3 votes
1 answer
116 views

Noether's theorem by a taste of logic [closed]

I am a mathematician and I asked this question briefly and my question became closed, may be - I don't know - because physicists don't used to apply the method of "proof by contradiction". ...
moshtaba's user avatar
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1 vote
3 answers
75 views

How much time does it take for an object to fall from space? [closed]

Let's say there's an object of mass $m$ in space, $h$ meters away from the surface of the Earth. $h$ is large enough that $g$ cannot be assumed to be constant. The acceleration varies according to ...
jazzblaster's user avatar
2 votes
2 answers
164 views

QFT introduction: From point mechanics to the continuum

In any introductory quantum field theory course, one gets introduced with the modification of the classical Lagrangian and the conjugate momentum to the field theory lagrangian (density) and conjugate ...
Xhorxho's user avatar
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1 vote
1 answer
58 views

Designing a thought experiment on Noether's Theorem [closed]

By Noether's theorem, in classical physics, conservation of total momentum of a system is result of invariance of physical evolution by translation. So logic says "if" there exists closed ...
moshtaba's user avatar
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1 vote
1 answer
82 views

Non-inertial frames in quantum mechanics

In classical physics, non-inertial frames necessitate adjustments to Newton's laws due to acceleration and rotation, yet in general relativity, Einstein successfully incorporates such frames. Why does ...
Vishnu's user avatar
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7 votes
3 answers
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In equation (3) from lecture 7 in Leonard Susskind’s ‘Classical Mechanics’, should the derivatives be partial?

Here are the equations. ($V$ represents a potential function and $p$ represents momentum.) $$V(q_1,q_2) = V(aq_1 - bq_2)$$ $$\dot{p}_1 = -aV'(aq_1 - bq_2)$$ $$\dot{p}_2 = +bV'(aq_1 - bq_2)$$ Should ...
Bradley Peacock's user avatar
1 vote
1 answer
54 views

Invertibility between generalized and actual coordinates

Chapter $1$, page $13$ of Classical Mechanics by Goldstein ($2^{nd}$ edition), he states the following after defining a transformation equation: "It is always assumed that one can transform back ...
Aditya Krishna Panickar's user avatar
-3 votes
2 answers
79 views

Meaning of $d\mathcal{L}=-H$ in analytical mechanics?

In Lagrangian mechanics the momentum is defined as: $$p=\frac{\partial \mathcal{L}}{\partial \dot q}$$ Also we can define it as: $$p=\frac{\partial S}{\partial q}$$ where $S$ is Hamilton's principal ...
User198's user avatar
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-3 votes
1 answer
56 views

Why aren't all objects and their images same in size?

Suppose there is an object in front of a convex lens and we know that the light rays from each point on the surface of object will converge at a different point and form an image. So that means that ...
Virender Bhardwaj's user avatar
3 votes
0 answers
46 views

Relating Brachistochrone problem to Fermat's principle of least time [closed]

When I came across the Brachistochrone problem, my teacher said we could relate it to Fermat's principle of least time. So, we could make many glass slabs of high $\mathrm dx$, and every slab has a ...
AANT's user avatar
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0 votes
1 answer
48 views

Why the interaction between system and thermal bath does not affect the energy levels of the system?

When we write down the full Hamiltonian of a system in contact with a thermal bath, it is as follows: $$H_{\text{total}} = H_{\text{system}} + H_{\text{system+bath}} + H_{\text{bath}}.$$ As our focus ...
user135580's user avatar
  • 1,068
1 vote
2 answers
65 views

Work performed by hydrostatic pressure

One should be able to show mathematically that the hydrostatic work done by an environment on an object undergoing a volume change $\Delta v$ should be $p \Delta v$, where $p$ is the (constant) ...
creillyucla's user avatar
2 votes
1 answer
87 views

How to compute the vector field from a potential in the complex plane?

I am watching this Youtube video and I have the following dumb question around 1:18:00: How do you draw the vector field for a given potential in the complex plane? He gives the potential $V(x) = x^4-...
Wyatt Kuehster's user avatar
1 vote
2 answers
110 views

Does Hamilton's principle allow a path to have both a process of time forward evolution and a process of time backward evolution?

This is from Analytical Mechanics by Louis Hand et al. The proof is about Maupertuis' principle. The author seems to say that Hamilton's principle allow a path to have both a process of time forward ...
Raffaella's user avatar
  • 353
0 votes
0 answers
15 views

Zero stress in $z$ components for thin surfaces

We can write the stress tensor as: \begin{equation} T= \left [ \begin{array}{ccc} \sigma_r & \tau_{r\theta} & \tau_{rz} \\ \tau_{\theta r} & \sigma_\theta & \tau_{\...
Remember's user avatar
  • 231
-1 votes
1 answer
82 views

Would a nearby electron be attracted/repulsed due to the oscillating $\vec E$ and $\vec B$ field of a passing electromagnetic wave? [closed]

I had just read up on the propagating electromagnetic wave equation, and realized that I do not know how to apply it in practice beyond knowing the equation... Suppose $$\vec E (x, t) = \begin{bmatrix}...
James's user avatar
  • 593
1 vote
3 answers
104 views

The conservative force [closed]

I read about the definition of the curl. It's the measure of the rotation of the vector field around a specific point I understand this, but I would like to know what does the "curl of the ...
Dirac-04's user avatar
0 votes
1 answer
93 views

Action-angle variables for three-dimensional harmonic oscillator using cylindrical coordinates

I am solving problem 19 of ch 10 of Goldstein mechanics. The problem is: A three-dimensional harmonic oscillator has the force constant k1 in the x- and y- directions and k3 in the z-direction. Using ...
SYD's user avatar
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0 votes
0 answers
26 views

Can a translational torque cause a change in rotational angular momentum? gyroscope example

Please confirm if my understanding is correct: The example of a gyroscope suspended from a pivot is a case in which translational torque causes a change in the direction of rotational angular momentum:...
Michael Horgan's user avatar
1 vote
1 answer
62 views

Vanishing virtual work done by non-holonomic constraints

I was reading classical mechanics by NC Rana. I was reading a topic on vanishing virtual work done due to constraint forces. How do you prove that the virtual work done by non-holonomic constraint ...
Aaron Nelson's user avatar
4 votes
2 answers
88 views

Why does my curry "bounce back" after stirring?

I recently cooked a big pot of curry, consisting largely of coconut milk, a bit of chicken stock and some vegetables. You can probably imagine that it was somewhat thick in consistency. The cooking ...
paulina's user avatar
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0 votes
1 answer
45 views

Is the Virial Theorem dependent on the classical Equipartition Theorem?

The Wikipedia entry for the Virial Theorem states: "*The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems ....
KDP's user avatar
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0 votes
2 answers
80 views

Generalized momentum

I am studying Hamiltonian Mechanics and I was questioning about some laws of conservation: in an isolate system, the Lagrangian $\mathcal{L}=\mathcal{L}(q,\dot q)$ is a function of the generalized ...
user1255055's user avatar
2 votes
3 answers
92 views

What's the need for 2 separate laws of motion when the first law is an special case of the second one? [duplicate]

The first law of newton tells us that a body shall remain unaccelerated when the net force acting on it is 0, but the second equation gives us the relation F=ma so, ain't the first law just an special ...
Manish's user avatar
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1 vote
1 answer
49 views

Finding Exterior Confining Pressure from Interior Pressure Point for a Solid Disk

Essentially, I've been wrapping the pictured object tightly with string to exert a confinement pressure on its exterior. It's been difficult however to make a good estimate of how much pressure is ...
Modestas Botha's user avatar
0 votes
2 answers
53 views

Consider a car going to a level curve while coasting(by disengaging clutch) is there any situation in which the speed of the car will increase?

Consider a car going to a level curve while coasting(by disengaging clutch) is there any situation in which the speed of the car will increase? (neglect the air resistence, assume the coefficient of ...
Zoro's user avatar
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