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; ...

learn more… | top users | synonyms (1)

0
votes
0answers
26 views

How to find velocities given Force

I have one large and one small body orbiting eachother, I can easily find the objects velocity $$v=\sqrt{aR}\hat{R}_\perp$$$$a=F_G/m$$ But if I add a third force how do I model the velocity, since it ...
0
votes
2answers
46 views

Partition function of a 3D vibrating string

Is the partition function of a 3D vibrating string a sum of discrete energies, an integral of an energy continuum, or both? $$ Z_{\text{disc}} = \sum_{k=1}^{\infty}g_ke^{-\beta E_k} $$ or $$ ...
0
votes
1answer
36 views

Why does mechanical energy have to equal zero to find escape velocity?

A object orbiting the earth has total mechanical energy equal to \begin{align*} E^{mech} = \frac{1}{2} m v^2 - \frac{GMm}{r} \end{align*} with $M$ the mass of the earth and $r$ the distance. My course ...
2
votes
2answers
405 views

Why does a wind turbine have only three blades? [duplicate]

Why not four or five or even more? Intuitively, the more leaves the more power. So, what is the reason?
-6
votes
0answers
27 views

Vector addition [on hold]

A pilot sets a course of 040$^{\circ}$ at an airspeed of $750$$km$$h^{-1}$. A wind blows SE at $140$$km$$h^{-1}$. Find the plane's ground speed and track. Can anyone illustrate this in a diagram?I ...
3
votes
2answers
84 views

Free rotation of a rigid body

So I am currently reading Fowles and Cassidy and there is something I'm confused about in the section about geometric description of free rotation of a rigid body. I will present the stuff first that ...
3
votes
2answers
137 views

Is the Legendre transformation a unique choice in analytical mechanics?

Consider a Lagrangian $L(q_i, \dot{q_i}, t) = T - V$, for kinetic energy $T$ and generalized potential $V$, on a set of $n$ independent generalized coordinates $\{q_i\}$. Assuming the system is ...
0
votes
1answer
38 views

Why is my Lyapunov exponent similar for single and double pendulum?

This is my first question here on stackexchange. I hope that I can be understood. If not, tell me and I will reformulate and fill in with details. I have simulated a single pendulum and a double ...
0
votes
1answer
31 views

Reversing time for a closed system of particles

For a closed system of particles, the lagrangian in classical mechanics is $$L=\sum \frac{1}{2}mv_a^2 - U(\mathbf{r_1},\mathbf{r_2}, \cdots)$$ For an arbitrary position function $x(t)$, to see the ...
-1
votes
0answers
24 views

Throwing the object around the Earth [closed]

You have to throw an object to a point diametrically opposite od Earth surface, take that Earth does not rotate and that it is perfect sphere. What angle to the ground and velocity must object have? ...
2
votes
0answers
28 views

What is the optimal slope for Archimedes screw?

The Wikipedia article has nice image showing how the Archimedes screw work: As I understand, the red balls do not fall down because they are in minima caused by the screw. Because of material ...
0
votes
0answers
20 views

Local conservation law involving Hilbert Transform in a classical field theory

Consider a nonlinear PDE of the form $$A_t +iA\mathcal{H}(|A|^2_x) +N(A) =0,$$ where the Hilbert transform $\mathcal{H}$ is defined as $$\mathcal{H}(|A|^2_x) \equiv P.V. \int_{-\infty}^{\infty} ...
0
votes
1answer
31 views

Tension along a curved surface [closed]

I'm curious what the tension in a rope will be when its exposed to a uniform load. Assuming a similar setup to this question what will the tension along the rope/tube be?
0
votes
0answers
23 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 ...
1
vote
1answer
34 views

Preventing Heat Escape

Is is possible to completely prevent heat from escaping from a closed container? Here is a diagram of vacuum flask, which tries to implement the design - Vacuum Flask prevents heat from escaping ...
0
votes
0answers
32 views

Bertrand's Theorem: Perturbative Methods Leading to $1/r^3$ Solution

My professor and I have been working on a proof of Bertrand's Theorem using perturbative methods. We have arrived at a solution yielding 1/r^3, which we had presumed to be an incorrect result. While ...
0
votes
0answers
18 views

Fun physics book for high school student [duplicate]

can anyone recommend me a physics book for a highschool student (not these typical school books) a book that will let you think mostly interested in theoretical /quantum physics done with the ...
0
votes
1answer
43 views

Classical Mechanics — Sign of work done

It seems that work has two possible ways to decide it's sign: Whether you take the perspective of the system or the surrounding (whether you consider work done on the system as positive, or work done ...
0
votes
1answer
23 views

Comparison of the effects of collisions from an NFL Nose Tackle and a Car with roughly the same momenta

If you get hit an NFL Defensive Tackle who runs at roughly 17mph (7.6m/s) it'd hurt a lot, but if you got hit by a normal car at 1.3mph (about 0.6m/s) it hardly hurts at all, and a collision from an ...
1
vote
1answer
41 views

How to determine plastic strain rate

Equivalent plastic strain rate is defined as $$ \dot{\bar{\epsilon}}=\sqrt{\frac{2}{3}\dot{\epsilon_{ij}}^{p}\dot{\epsilon_{ij}}^{p} } $$ Where, $ \dot{\bar{\epsilon}}$ is equivalent plastic strain ...
0
votes
2answers
46 views

What is the meaning of this definition of potential energy?

The isolated system of particles is being observed. In the coursebook, $\vec F_\mu$ is by definition the vector sum of forces of all other particles acting on $\mu$-th particle. Usually, potential ...
0
votes
1answer
61 views

A course in Lagrangian Mechanics [duplicate]

I would like to know: what are some of the best introductory books to Lagrangian Mechanics?
1
vote
2answers
73 views

Classical trajectories that are not a minimum of the action [duplicate]

Are there physically realizable dynamical systems where the true trajectory is not a minumum action trajectory? Formally, Lagrangian mechanics only requires that the trajectory be an extremum (or ...
1
vote
0answers
27 views

Why does not the optical fiber break? [duplicate]

Glass is a very fragile object. So why does not the optical fiber break? Everytime I take them, I am worried about this problem.
1
vote
0answers
35 views

Time evolution of a classical system

For a harmonic oscillator the Liouville operator is given by $$L = p \partial_q- q \partial_p.$$ Now I have a phase space distribution $f(t,q,p)$ for which it holds (in general) $$f(t+\tau,q,p)= ...
0
votes
1answer
20 views

Equations of motions uneven see-saw

How do I set up equations of motions for a see-saw where the distance between the masses $m_1,m_2$ to the pivot are given by $\ell_1, \ell_2$, respectively? My idea was to first set one of the masses ...
0
votes
2answers
49 views

Proof of vertical and horizontal velocity component in projectile motion

Why is it that $v\cdot sin(x)$ gives the vertical component and $v \cdot cos(x)$ gives the horizontal component, where $v$ is the speed? What logic is there behind it, or even better is there a proof ...
0
votes
0answers
14 views

Determining the range of values for separation angle (Landau problem)

I encountered a problem while reading the following exercise from the second Landau & Lifshitz volume: Determine the range value in the $L$-system for the angle between the two decay particles ...
1
vote
0answers
6 views

Effective length factor of a polymer in solution

If one wants to calculate the force needed to buckle a polymer in solution with Euler buckling, what would the effective length factor be? The polymer is free to move and rotate in solution as it sees ...
0
votes
1answer
31 views

Vector representation of angular quantities?

In the world of pure rotation, a vector defines an axis of rotation, not a direction in which something moves. Does it means that angular quantities like angular momentum, angular speed, torque etc ...
1
vote
0answers
38 views

question regarding work energy theorem [closed]

The question says A smooth track in the for of a quarter circle of radius 6 lies in the vertical plane. A ring of weight 4N moves from $P_1$ to $P_2$ under forces $F_1$,$F_2$ and $F_3$. $F_1$ is ...
3
votes
1answer
71 views

Confusion about imposing constraint in the action

I'm totally confused by one thing. I know that I probably shouldn't be confused about that, but at the moment I don't quite know what fails in the following: Suppose we have a particle of unit mass ...
3
votes
1answer
58 views

Can a “flat function” be a particle trajectory? [duplicate]

Recently I came across the concept of a flat function, which is a smooth function $f:\mathbb{R}\to\mathbb{R}$ all of whose derivatives vanish at a given point $x_0\in\mathbb{R}$, the canonical example ...
0
votes
3answers
75 views

Having trouble understanding spectral lines

In my notes I wrote that Rutherford's model of the atom could not explain spectral lines, because that is what my textbook says. I'm not really sure about the details of spectral lines though. I know ...
0
votes
2answers
79 views

Definition for potential energy

I came across this definition for potential energy: If we let $T$ be the Kinetic energy, we have that: $$T = \frac{1}{2}mv^2 \implies T = \frac{1}{2}m{x'}^2$$ $$T'= mx'x'' = F(x)x' \implies \\T = ...
3
votes
3answers
209 views

Constructing Lagrangian from the Hamiltonian

Given the Lagrangian $L$ for a system, we can construct the hamiltonian $H$ using the definition $H=\sum\limits_{i}p_i\dot{q}_i-L$ where $p_i=\frac{\partial L}{\partial \dot{q}_i}$. Therefore, to ...
4
votes
3answers
190 views

Two different time periods for a movement with constant acceleration?

I'm studying for my physics exam and I keep running into the same problem. It's so specific I have no idea how to phrase it in a Google or stack exchange search, and I've already wasted 2 hours on it. ...
1
vote
1answer
144 views

How is quantization related to commutation? [duplicate]

How are commutation (of observables) and quantization related? Reading about the Stone-Von Neumann Theorem, it seems that commutativity is the classical limit of quantum mechanics, and hence ...
0
votes
2answers
92 views

Galilean relativity & the road to special relativity

Firstly, I just want to make sure that I've understood the notions of relative and absolute quantities correctly. Elementary analysis shows that position and velocity are relative quantities. Indeed, ...
0
votes
2answers
29 views

Kinetic energy dissipation in braking a vehicle

Let's say a vehicle that weighs 20t is hauling along at 50m/s and we want to brake it down to a full stop. The kinetic energy we need to dissipate into heating up the brakes is ...
3
votes
2answers
88 views

Derivation of law of inertia from Lagrangian method (Landau)

I'm reading Landau's Book. He tries to conclude the law of inertia from the Lagrange equations. For that, he argues (by nice suppositions about space and time), that the lagrangian must depend only ...
0
votes
1answer
36 views

How does the masless pulley gets the force from rope?

I have seen whenever we solve for forces on pulley by rope we take the force on pulley exactly as the tensions in the rope around it. But , why do we do this ? Exactly how does the rope exerts forces ...
2
votes
2answers
105 views

Detailed conditions for symmetries of Lagrangian

Edit: To clarify the question, I am asking why we are justified in calling a continuous symmetry a symmetry of a system when it changes the Lagrangian by a total derivative of a function of $t, q(t)$ ...
1
vote
1answer
50 views

How to find Tangential/Radial/Angular Velocity for motion in any curve?

Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction ? If so why ? Please try to give a different ...
0
votes
0answers
25 views

How is angular momentum conserved in this proton+water scenario?

Consider a universe consisting of only one water molecule and one proton. ...
0
votes
2answers
44 views

When considering the acceleration as constant? [closed]

I'm solving a simple dynamic exercise, exercise says: "What is the absolute value of the force necessary to speed up a 500kg mass subject to 1600km/h in 1,8s, with the object from rest?" Then I had ...
4
votes
0answers
155 views

What exactly is the relationship between the symplectic 2-form and the frequency of leaves of integrable systems in classical mechanics?

In classical mechanics we equip a differential manifold with a closed symplectic 2-form $\omega$. The symplectic leaves of integrable systems also have a unique frequency, in literature denoted ...
19
votes
3answers
2k views

Why does a Yo-Yo sleep, and then awaken?

What are the mathematics / mechanics principles behind a sleeping Yo-Yo, and in particular, what changes with a wrist-snap flick that causes it to "awaken" and return to your hand?     ...
0
votes
1answer
50 views

By what factor would you have to slow down time for water to feel like glass?

I have been told that though glass seems like a solid, it is somehow, in theory, a liquid -- but is just somehow a liquid that is so thick that it appears to be solid. (Of course --- if this premise ...
0
votes
0answers
23 views

Bezier curve and deceleration

I have a question regarding calculation of a bezier curve. I'm programming an app where in there's continuous straight line motion of a vehicle at a constant speed. (Let's call it 'u'). When the user ...