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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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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116 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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97 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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59 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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95 views

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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40 views

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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105 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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2answers
138 views

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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77 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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30 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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74 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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145 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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125 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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87 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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74 views

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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95 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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21 views

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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57 views

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 ...
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30 views

classical extrema to Lagrangian field equation

Local extrema to the classical Lagrangian field equation are minima and are termed instantons. In classical field theory we do not distinguish between global and local extrema of the action. Can we ...
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67 views

Average energy of a damped-forced harmonic oscillator during a period t

In my textbook, it's stated without proving the following identity for a classical damped-forced harmonic oscillator: $$ \bar{E}^t = \bar{T}^t + \bar{V}^t = 2 \bar{T}^t \, , $$ which states that ...
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37 views

What is special about quantum entanglement? [duplicate]

Get two pieces of paper. In secret write the same number on both papers. Transfer one paper to the Moon. Look to the paper which is left at the Earth. Voila! We know what is on the Moon paper. The ...
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210 views

How does height of a parachute affect air resistance compared to circumference or diameter?

I'm trying to find out how much a double in height (making it more ovular or oblong in shape) of the parachute affects air resistance compared to a double in circumference or diameter. Can someone ...
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204 views

Why is the Hamilton-Jacobi equation important? [closed]

Someone may say it is related to the Schrodinger equation. Okay, let us forget about quantum mechanics. So, if we confine ourself to classical mechanics, why is the Hamilton-Jacobi equation important ...
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71 views

Finding the configuration space and degrees of freedom of spherical pendulum

Suppose we have a spherical pendulum tethered to the origin in $\mathbb{R}^3$ where the length of the rod is a time varying function $l(t)$. What is the configuration space of this system, and how ...
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41 views

Making Pudding; A complicated non-equilibrium statistical process?

There are a lot of non-equilibrium processes examples given in physics literature. But some processes that are present in everyday life are not treated. As an example, the formation of pudding can be ...
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61 views

Is rigid body rotation an integrable problem?

Is there chaos? The configuration space is 3d. There are four constraints, namely, the energy, the three components of the angular momentum. So there are still two degrees of freedom.
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75 views

Why aren't the weights of the beads considered in this equation?

I was solving this problem: A ring of mass $M$ hangs from a thread and two beads of mass $m$ slide on it without friction.The beads are released simultaneously from the top of the ring and slides ...
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44 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 I'...
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31 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.
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16 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 ...
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55 views

Normal coordinates for harmonic approximation (classical lattice vibration)

I am reading Jenő Sólyom's "Fundamentals of the Physcs of Solids" vol. 1. and i am very much stuck at this point (chapter 11.3.2 in the book): In the harmonic approximation the potential energy of a ...
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29 views

Conserved charge for boosts? [duplicate]

In (3+1) dimension Poincare group has three types of Symmetries : a) Four space-time translations b) Three spatial rotations and c) Three boosts Among them, (a) implies "conservation of 4-...
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89 views

Fluid mechanics -Question about boundary?

Problem statement: A two-dimensional fluid stream of thickness $S$ and velocity $c$ (evenly distributed through the thickness of the stream) falls on a stationary plate and gets separated. Calculate ...
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39 views

When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)? [duplicate]

When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)?
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128 views

Angular acceleration as a function of torque

I know that the angular momentum $\mathbf{L}_{cm}$ with respect to the centre of mass of a rigid body can be expressed as $I\boldsymbol{\omega}$ where $I$ is the inertia matrix and $\boldsymbol{\omega}...
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205 views

Components of acceleration in spherical polar co-ordinate [closed]

I wanted to calculate two component of acceleration in polar co-ordinate. Starting from the lagrangian $$L= \frac{1}{2}m( \dot{r} ^{2}+ r^{2} \dot{ \theta } ^{2} ) -V(r, \theta )$$ I ...
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119 views

Is there a speed limit for objects falling in gases or liquids? [duplicate]

Let $o$ be a spherical object with mass $m$ and surface $s$. Let $g$ be the gravitational acceleration and $h$ the height. Let the gas where we drop $o$ in have density $d$ and pressure $p$ at ...
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71 views

Hamiltonian flow?

I was wondering what the Hamiltonian flow actually is? Here is my idea, I just wanted to know if I am correct about this. So let $(x(t),p(t))' = X_{H}(x(t),p(t))$ are the Hamilton's equations and $...
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55 views

How to find the spring coefficient of a simply supported beam?

So I've been searching wikipedia and google but nothing can show how to find the spring coefficient of a simply supported beam with a uniformly distributed load. The spring coefficient, $k$, is ...
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44 views

Does the force of releasing the latch of a spring-latch contraption affects the force generated by the spring?

There is this contraption in my class, where a rod is attached to a latch and a spring. By pulling the latch back behind a piece of metal, the latch is secured, the rod if pulled back and the spring ...
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93 views

Physical interpretation of the relative displacement tensor?

I've resolved a relative displacement tensor into a strain tensor and a rotation tensor, where the strain tensor is: $$ \varepsilon_{i,j} =\begin{pmatrix} 0.2 & 0 & 0 \\ 0 & 0.8 &0.4\...
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532 views

What is a “Reversed Effective Force”?

I have some confusion about the "Reversed effective force" as it appears in the derivation of D'Alembert's principle. In Goldstein d'Alembert's principle is given as: $(F-\dot{p}) \cdot \delta r = 0$...
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156 views

When to use Hamiltonian vs Lagrangian?

I currently studying the Lagrangian and Hamiltonian formalisms in classical mechanics, but something I'm not seeing is how do I know which one to use in a given problem? After I find the Lagrangian, ...
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336 views

Effect of Eath's rotation on a ball thrown upwards [duplicate]

Since the Earth is rotating it should have acceleration (in the sense that there is change in direction of velocity). So if we throw a ball upwards won't this acceleration affect its trajectory in ...
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347 views

What are the mathematical models for force, acceleration and velocity?

In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
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130 views

Relative kinematics and laws of Newton

I am an engineering student and currently taking a class on kinematics and dynamics. I study at a German university so it may be that I don't translate everything correctly. In the first module of ...
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55 views

Thermal de Broglie wave length

If we refer to this wiki page thermal de Broglie wave length, we can see there are two expressions. One is derived using equipartition theorem, which makes perfect sense. The other one used $\pi kT$ ...
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Does the additivity property of Integrals of motion and Lagrangians valid in all situations?

I would like to know if the additivity property of an integral (constant) of motion valid in all situations ? It works for energy but does it work for all other integrals of motion in all kinds of ...
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Motion in a vertical circle and forces in polar coordinates

Suppose a particle with mass $m$ is whirled at instantaneous speed $v$ on the end of a string of length $R$ in a vertical circle. Let $\theta$ be the angle the string makes with the horizontal. I know ...
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278 views

Explanation of force amplification inside a solenoid

For a system being actuated by a motor, the force can be amplified by gearing. The energy is being used for force instead of distance, so it produces more torque but moves slower. For a system being ...