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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Reference books for classical mechanics with good number of solved examples

I am looking for some classical mechanics reference book with a good number of solved problems.
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787 views

Conservation of linear and angular momentum

Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
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12 views

How long does it takes for an object to slide on an incline ramp?

I hope I am asking this question in the correct site. Here is my question: if there is an incline at $70$ degrees, the object's friction is $\mu = 0.1$, and the incline is $1$ meter long, how long ...
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3answers
48 views

Who does work while walking?

While walking the work done by friction is zero. But who does the work, actually? How someone is getting displaced? This situation also arises when someone climbs without slipping or is climbing a ...
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4answers
64 views

Since everything with mass exerts a gravity force on everything else, why do objects float in outer space?

For example, if you were to go out into deep space, and just slow down and stop your rocket. Everything inside the rocket that's not strapped in, starts floating. Why is that if every object has mass ...
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2answers
215 views

How do I figure out the momentum of a water balloon when it reaches the person I am throwing it at?

Recently an experiment was performed in which myself and a partner filled a water balloon and threw it back and forth at each other without breaking it. We gradually increased the distance at which it ...
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1answer
75 views

Heuristic equation for Friction force between materials

I'm programming a game where different types of objects will be sliding over different types of terrains (Top-down in two dimensions). At my current level of physics education we are given the ...
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2answers
58 views

Why isn't jumping against a wall an elastic collision?

According to this calculator http://www.abecedarical.com/javascript/script_collision1d.html when low mass object hits high mass object it is reflected gaining opposite velocity almost the same as ...
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1answer
51 views

If you dig a deep tunnel, will the rock sublimate?

If a tunnel is dug deep inside the crust (but before reaching places where the rock is liquid), how will the enormous downwards pressure manifest itself? Will the difference in pressure ...
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25 views

Energy and momentum as partial derivatives of on-shell action in field theory

According to L&L, if we fix the initial position of a particle at a given time and consider the on-shell action as a function of the final coordinates and time, $S(q_1, \ldots, q_n, t)$, then... ...
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1answer
87 views

In a 2-body problem, when is the moving path closed?

In a 2-body problem is it true that, in all situations, the moving path is closed? In which cases are the paths closed? Fixing the coordinate system or fixing one of the bodies gives us different ...
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46 views

Which way to lean when driving a gokart?

Given a car that has two lines of wheels, the center of gravity at constant height above the ground, constant turn angle and given surface and wheel material. What is the maximum speed the car can ...
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1answer
20 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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2answers
75 views

What is the “associated scalar equation” of equations of motion?

In an essay I am reading on celestial mechanics the equations of motion for a 2 body problem is given as: $$\mathbf{r}''=\nabla(\frac{\mu}{r})=-\frac{\mu \mathbf{r}}{r^3}$$ Fine. Then it says the ...
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2answers
65 views

Force Diagram for K&K 2.13 [on hold]

I have been (independently) working on Problem 2.13 in Kleppner and Kolenkow's An Introduction to Mechanics and come to an answer which conflicts with the hint the authors provided in the book. The ...
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3answers
480 views

Is it possible to deduce the conservation of angular momentum from the conservation of energy?

Is it possible to deduce the law of conservation of angular momentum from the law of conservation of energy? If possible, by what sense the conservation of angular momentum has the status of law, if ...
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1answer
72 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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1answer
186 views

Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
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1answer
36 views

What does an $n$-body system with constant $T$ and $U$ look like?

Can someone give an example of a system where the kinetic $T$ and potential $U$ energy are constant (but not zero)? Here's what I have in mind: Say you have $n-1$ satellites of negligible mass ...
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3answers
92 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
56 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
20 views

Degrees of Freedom for an Asymmetric top

How many degrees of freedom does an asymmetric top have if it is rotating about a fixed point?What are the generalised coordinates used then?
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1answer
38 views

Liquid Column “Recoils” in a Sealed Cylinder When Hit by a Piston — Is it Possible?

Consider a cylinder filled partially with a liquid (e.g. water). The cylinder is sealed, and is at held at room temperature (e.g 298K). At equilibrium (or when no external disturbance is imparted to ...
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2answers
205 views

Why is this the volume flow rate per unit area?

In fluid mechanics we consider a fluid filling a region $D\subset \mathbb{R}^3$ together with a function $\rho : D \times \mathbb{R} \to \mathbb{R}$ called the mass density such that for any ...
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36 views

Intuition behind the principle of virtual work

To derive Lagrange's Equations we need the principle of virtual work first. This principle states that whenever a system of $K$ particles is constrained to a submanifold $\mathcal{M}\subset ...
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2answers
156 views

Strain energy density in index notation

The strain energy density is defined as $$dU = \int_0^{\epsilon_{ij}} \sigma_{ij} d \epsilon_{ij}$$ (see Reddy "Energy Principles and Variational Methods in Applied Mechanics", 2nd Ed, 4.11). Assuming ...
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29 views

Gauge formalism in rigid body mechanics

When doing calculations in rigid body mechanics, it is necessary to choose an origin to calculate torques and angular momenta. However, the underlying dynamics does not depend upon the choice of that ...
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4answers
366 views

Are Lagrangians and Hamiltonians used by Engineers?

Analytical Mechanics (Lagrangian and Hamiltonian) are useful in Physics (e.g. in Quantum Mechanics) but are they also used in application, by engineers? For example, are they used in designing bridges ...
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35 views

How to prove that generalized coordinates are independent?

I know that the generalized coordinates obtained after taking into account the constraint forces are independent. How can I prove this?
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1answer
45 views

How can I derive the Hamiltonian of simple harmonic oscillator from this Lagrangian?

I'm working through Leonard Susskind's Theoretical Minimum: Classical Mechanics and I can't seem to understand how the Hamiltonian of a simple harmonic oscillator is derived from the following ...
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0answers
22 views

Equations of motion for controlled/driven classical systems? Does D'Alembert's principle apply?

I'm puzzled about how to derive the equations of motion for certain classical systems where some entity is controlling some of the DOFs. For example, consider a double-pendulum, with lengths $l_1$ ...
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1answer
399 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: ...
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29 views

Examples of projection of angular velocity

I am looking for examples where the projection of angular velocity vector onto a different axis, has some interesting physical meaning in day-to-day contexts. For example, if a gramophone turntable ...
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2answers
369 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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4answers
194 views

Detecting absolute motion inside a box

This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows. ...
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5answers
301 views

Why can't we obtain a Hamiltonian by substituting?

This question may sound a bit dumb. Why can't we obtain the Hamiltonian of a system simply by finding $\dot{q}$ in terms of $p$ and then evaluating the Lagrangian with $\dot{q} = \dot{q}(p)$? Wouldn't ...
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1answer
186 views

Push a box in a plane with friction. How to deal with the rotation?

Suppose I have a box (say, length-1m, width-1m, height-0.5m) on the plane with friction. I can apply a horizontal force in on the surface of the box. If the force doesn't pass through the center of ...
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1answer
39 views

Does lever needs gravitation to work? [closed]

Simple question - Does lever needs gravitation force to work or it just needs fulcrum and could work in vacuum as well?
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3answers
80 views

What is the work done against a force?

Suppose a particle travels a path $\gamma : I\subset \mathbb{R}\to \mathbb{R}^3$ subject to a force $\mathbf{F}: \mathbb{R}^3\to T\mathbb{R}^3$, then we know that we define the work done by the force ...
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1answer
844 views

Why does a cuboid spin stably around two axes but not the third?

Let $C$ be a cuboid (rectangular parallelepiped) with edges of lengths $a < b < c$. Consider an axis that passes through the centers of two opposite faces of $C$. There are three such axes, ...
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2answers
82 views

Why does pitch in a helicopter take effect 90 degrees later?

In a helicopter if you want to give it a forward pitch, you change the angle of the blades when it is in this position ---- So the two blades experience unequal lift and because o gyroscopic ...
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2answers
73 views

Force applied to an inclined plane

Below is a picture of the problem. Any guidance would be helpful. This problem isn't actually from any assignment, per se. I'm hoping that, by understanding this, it'll help me to understand a ...
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0answers
38 views

How can one diagonalize the second variation of action?

Suppose we have action $S[q]$ and its stationary path $q_s$, I want to find the orthonormal paths $\psi_n$ that can diagonalize the second variation of the action $S[q]$. How to do that? Thanks
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4answers
511 views

D'Alembert's Principle: Necesssity of virtual displacements

Why is the D'Alembert's Principle $$\sum_{i} ( {F}_{i} - m_i \bf{a}_i )\cdot \delta \bf r_i = 0$$ stated in terms of "virtual" displacements instead of actual displacements? Why is it so necessary ...
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2answers
104 views

How can I derive this Hamiltonian?

I have a Lagrangian $L$, a momentum $p$ and a Hamiltonian $H$: $$L=\frac m 2(\dot z + A\omega\cos\omega t)^2 - \frac k 2 z^2$$ $$p=m\dot z + mA\omega\cos\omega t$$ $$H=p\dot z - L=\frac m 2 \dot ...
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3answers
82 views

Configuration manifolds and constraints

In Classical Mechanics there's this notion of configuration manifold. Although I've heard about that a lot and although I often use that concept, I'm not sure I really understand them well because ...
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1answer
79 views

Could the center of the combined mass of the entire galaxy change if there were no external forces acting on that galaxy?

Everything in the galaxy orbits the center of the combined mass of the entire galaxy. So could the center of the combined mass of the entire galaxy change if there were no external forces acting on ...
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126 views

Story about a mathematician, a dinner party, and the three-body problem

I remember dimly hearing a story, coincidentally also at a dinner party, and I was trying recently to track the details down with no success. I was hoping someone here might have also heard this story ...
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1answer
63 views

Understanding action reaction in an example

When I move an object that object should move me as well. I tried standing on a skateboard to reduce friction, and holding a heavy barbell, move myself away from it (while still holding it) but I ...
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1answer
105 views

“A Crash Course in Lagrangian Dynamics”. Is it still available online?

In an Amazon review of "Schaum's Outline of Lagrangian Dynamics" I found this: I recommend that you type "Lagrangian Dynamics" into Google and look at some of the excellent sets of lecture notes ...