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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Intuition behind Airy waves dispersion relation

Using Airy wave theory, one can derive the dispersion relation of water waves (under some physical assumptions): $$ \omega^2 = gk\tanh{kh} $$ where $k$ is the wave number, $h$ the distance from the ...
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61 views

Clarification on conservation of energy for (or internal potential energy of) $N$ particle system

In Goldstein's Classical Mechanics, it says: Consider now the right-hand side of Eq. (1.29). In the special case that the external forces are derivable in terms of the gradient of a potential, the ...
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Newton's mechanics. Axioms, postulates, etc

I am trying to write all the assumptions or postulates to set up Newton's mechanics: 1.- The space is infinite, continuous, homogeneous, isotropic and 3-dimensional. By this way, we assume that the ...
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Is it proper definition of the free motion? The orbit of free motion is a free group [closed]

That's what I wrote in my notes but I don't understand this definition, I've studied group theory but free groups were not included. Can someone explain this definition, please?
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First problem from Slater & Frank book on mechanics [closed]

I can't solve the very first problem and have no one to help me (I'm self-studying it in these vacations): "1. A particle moves in a vertical line under the action of gravity and a viscous force ...
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Classical Mechanics Resources [duplicate]

I hope that my question doesn't violate the posting rules. I was wondering if any of you have any resources (websites, books, etc.) for classical mechanics. My first week of classical mechanics has ...
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28 views

Why do very small balls attached to a tiny spring propel themselves in hardly moving fluids? [duplicate]

I recall watching a youtube video about a ball with a spring on the idea propelling themselves through stable fluids without any assistance, even if we make sure the spring isn't moving in the ...
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28 views

Which of Landau's books are suited for undergraduates? [closed]

Seeing how well-received Landau's books are, I want to know if any of them are suited for undergraduates.
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What causes the balloon to pop when we push with needle onto it's surface?

I am a bit puzzled because I can see two possible reasons, first one is more common and the other one makes sense too, so here they go: 1) balloon pops because of the fact that after pressure is ...
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14 views

Ski treadmill materials

This ski treadmill is not much of an incline, but it still allows people to ski and carve out turns. What materials have such a low coefficient of friction, yet allow higher friction at higher ...
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Relation between solvent accessibility and brownian motion

Assume one has a molecule (made of nodes) inside a solvent. If one tries to model the average effect of the interaction between the molecule and the solvent, one has two effects: 1- Friction term on ...
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When the equations of motion are not unique (eg. when they are given by eigenvectors), which will the free particle adhere to?

For this question I think it will be easier to express the usual equation describing the motion of a "free particle,"--viz. $g_{ij}\dot{x}^i\dot{x}^j$--in matrix form as follows: ...
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Maximum possible acceleration value on a ball in volleyball game

I have been examining this subject on web but could found enough information yet. I have to make a decision on choosing "range" for accelerometer which will measure acceleration value of ball in ...
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24 views

Pivot Point Equations [closed]

Assume we have a platform fixed to a pivot point: -Forgive the crude image- We use 2 rods, either side of the pivot point, but at different distances from it. If we were to lift ROD 1 by a certain ...
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46 views

Acceleration in a space capsule which is falling to the earth [closed]

At first I apologize for asking such a career killing question in such an elite platform. Today I tried to prove something to four graduated engineers which I will mention below. The argument ...
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should transverse and longitudinal phonon velocities be equal for this mass spring system?

Let's say we have a cubic lattice of identical masses $m$, each connected to its 6 nearest neighbors by identical spring constants $k$. Essentially, the problem is I get an eigenvalue problem with ...
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26 views

Stewart platform formulas [closed]

What kind of formulas/equations are commonly used to implement Stewart Platforms in electronics and mechanics? Using a co-ordinate system, how would you determine the position of each actuator, etc?
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Two compound bars connected in series hanging vertically [closed]

I have a steel and a copper connected in series. We know the original length, cross area and young modulus of both bars. Now we hang it vertically, connected the upper end of copper to the ceiling and ...
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Does more surface area mean more traction?

I came across this question when considering new vehicle tires in a snowy environment. It appears that big off-road tires have very deep treads which greatly increase the surface area of the tire. ...
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Are the generalized coordinates in Lagrangian mechanics really independent?

In Goldstein's Classical Mechanics, Chapter 2.3: Derivation of Lagrange's Equations From Hamilton's Principle part of the derivation involves each of the generalized coordinates being independent. $$ ...
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Rotation, translation or both. [closed]

the square is the same material throughout, equal mass distribution. In this case, will the object rotate, translate or both and why ? Thank you.
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Internal energy in classical and quantum mechanics [closed]

What is the difference between classical and quantum mechanics of rotational, translational and vibrational energies?
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Height of water in vessel containing gas [closed]

The question reads- Thin walled Cylinder of height h, mass m and cross section A filled with gas and floats on water. Now due to leakage depth of submergence increases by $\Delta h$. $P_o$ is the ...
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17 views

Finding maximal angle after elastic collision [closed]

Let $m_1=400gr, m_2=600gr$ represent the masses of two balls. the two balls are hanging from the ceiling ($m_1$ is right to $m_2$), and then someone pull to the right side the $m_1$ ball in an angle ...
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Is time-1 map of a Hamiltonian vector field on a cylinder always twist?

I have a one degree of freedom analytic Hamiltonian $H(q,p)$ defined on a semi-infinite cylinder, i.e. $(q,p) \in \mathbb{T} \times \mathbb{R}^{+}$, such that all level sets $H(q,p)=c$ are closed ...
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A mysterious conserved quantity for a central potential

In teaching a course in classical mechanics and I have come across (from my predecessor) a to me mysterious conserved quantity. We are considering a gravitational (or electric) potential with the ...
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125 views

Friction in Lagrangian formulation

We know the Lagrange equations are: $$\frac{\partial \mathcal{L}}{\partial q_i}-\frac{d}{dt}\left(\frac{\partial \mathcal{L}}{\partial \dot{q_i}}\right)=0.$$ Then, when we add friction in there, we ...
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36 views

Law of conservation of momentum , elastic collision [closed]

In Law of Conservation of momentum , elastic collision occurs only in an isolated system. A case defined as,when Object A comes with initial velocity and collides with object B which is in rest V= ...
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0G(No motion) scenario detection using Accelerometer and Gyroscope [closed]

I have a gyroscope and accelerometer which I am placing on the wheel of a bicycle to detect the 0G or standstill (when the bicycle exactly reaches to rest) of the wheel. I put the sensor at a R/2 ...
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67 views

What is the origin of the Maxwell's wheel? [closed]

Tried to find it online, but nothing. Every refers to it and that it's named after the famous James Clerk Maxwell (of the maxwell electromagnetic laws and some other things) but it's like the ...
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42 views

Generating function as a prove of a canonical transformation [closed]

Does the existence of a generating function $ F $ prove that a given transformations is canonical? How? The thing is: Show that the transformation is canonical $$ Q=p+iaq $$ and $$ ...
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1answer
54 views

Consider a particle of reduced mass $\mu$ orbiting in a central force with $U=kr^n$ where $kn>0$ [closed]

Consider a particle of reduced mass $\mu$ orbiting in a central force with $U=kr^n$ where $kn>0$. (a) Explain what the condition $kn>0$ tells us about the force. Sketch the effective ...
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1answer
65 views

Equations of motion for double spherical pendulum simply?

I am attempting to simulate a double spherical pendulum, i.e. a combination of the spherical pendulum and the double pendulum. I understand that the equations of motion can be derived via the ...
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32 views

Relation between force and torque for a set of gears/bicycle

If there are 2 gears meshed together and they are of different sizes, then rotating the smaller one will make the larger one spin with a smaller angular velocity but with more torque. And the opposite ...
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What is the difference when we measure torque/angular momentum about a point and about an axis?

When do we measure torque about an axis and when do we measure torque about a point?Whats the difference? I tried searching this on google but did not get satisfactory answer.
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What's the point of hamiltonian mathematical formalism of classical mechanics? [duplicate]

Just what the title asks. What are the applications of it?
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70 views

A bead is threaded on a frictionless vertical wire loop of radius R

The question is the very last sentence at the end of this post. In this post, I'll demonstrate how I reach to a contradiction(the conditions mentioned in conjecture 1 should be satisfied by all ...
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How will hovercraft work on Mars?

The facts are: On Mars atmosphere pressure is way much lower than on Earth. To hover hovercraft blows air under itself to create air cushion. This air cushion as I understand must have enough ...
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Finding equilibrium points in two dimensional potential [closed]

Ok so suppose I have a two dimentional potential. I want to find the stable and unstable equilibrium points and to decide which is which. So I know that I can derive them by finding the gradient of ...
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73 views

Proof of Lagrangian

I'm having some trouble with some math on a problem for a physics class (looking for help with some partial derivatives, not an answer). Let $$L'=L+\dfrac{dF}{dt},$$ where $L$ is a Lagrangian and $F$ ...
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27 views

Taylor vs Goldstein [duplicate]

I'm trying to select a mechanics book for self-study. I have some math background (linear algebra and calculus among other things) and I want to pick a book that won't skip over the math. I would ...
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1answer
56 views

Navier-Stokes: equation or equations [closed]

In textbooks and papers, you see both forms: the Navier-Stokes equation and the Navier-Stokes equations. Which one is correct and why?
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1answer
112 views

If a body slides down a frictionless inclined plane what will be the net normal force?

If a body(m) slides down a frictionless inclined plane (M), will the net normal force between the ground and the inclined plane be (M+m)g ? I feel it should be less than (M+m)g. This is because one ...
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96 views

Conserved quantities for the system, classical mechanics

In certain situations, particularly one-dimensional systems, it is possible to incorporate frictional effects without introducing the dissipation function. As an example, find the equations of motion ...
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66 views

Canonical Momentum Conjugate vs. Momentum

I stumbled upon this while reading about Legendre Transforms today. So consider an n-particle system. The Lagrangian is a function of $ q_i$'s and $\dot q_i$'s. If you consider the manifold $M$ where ...
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Potential Energy of two masses

If two particles with masses $m_1$ and $m_2$ interact and are located at $\vec{s_1}$ and $\vec{s_2}$ have their potential energy $U$ defined by the modulus of their position vectors, how would I ...
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49 views

Hollow Iron pipe electromagnet? [closed]

How strong would a electromagnet be if I use a hollow Iron pipe as the core? The thickness of the pipe will be 2-3 cm. How much weaker would this electromagnet be compared to a non-hollow ...
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85 views

Contradiction in a simple torque/rotation problem - two ways of calculating external force don't agree

Suppose we have a rigid system of two point objects (both of unit mass) connected with a massless rod, with the objects horizontal on the x axis, at a distance $r_1$ and $r_2$ from the origin, ...
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Preservation of phase space volume: the extension from “small” times to generic times

Having a classical system whose evolution is described by \begin{equation} \dot{\phi_t}(x) = f(\phi_t (x))\\ \phi_0 (x) = x \end{equation} denoting with $\phi_t (x)$ the evolution for a time t of the ...
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Solving for position of a SO(3) rotating object, given the integrable functions for components of angular velocity along the principle axes

Assuming that you have approximated or solved the Euler's Equations for components of angular velocity along its principal axes of inertia $x$, $y$ and $z$ - i.e. in the coordinate system that is ...