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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What is the physical interpretation of this quantity?

For the second order ODE governing the position of a projectile subject to air resistance $$ m\frac{d^2x}{dt^2} +k\frac{dx}{dt}+mg=0 \quad k>0, \> x(0)=0, \> x'(0)=V>0 $$ a ...
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15 views

Conservation of linear momentum for a system with a small mass inside a cylinder

Say that you have a thin hollow cylinder with mass M on a flat ground. Inside the cylinder on its wall is a point-sized object with mass m. Initially everything is at rest. Then the cylinder and the ...
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13 views

Functional relationship of pressure and position(1d)

so today I started doing my research on oscillations in a course on advanced mechanics. The experiment was to mathematically model the speed of sound in air and experimentally prove the usability of ...
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14 views

Can you pull and also grind a material through a length of cylinder? [on hold]

I want to take plant matter for instance, and instead of splitting up the grinding phase and feeding through a tube phase (using a screw inside the cylinder), I'd like to combine them into one. So ...
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41 views

Pdf of particles in phase space

I am from a non-physics background and hence have difficulty in grasping the concepts some of which I need to apply in signal processing. Link1 and Link2 discuss about Liouville theorum and phase ...
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40 views

Cutting a circle and moving endpoints

A metal (or otherwise, suitably elastic) circle is cut and the points are slid up and down a vertical axis as shown: How would one describe the resultant curves mathematically?
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2answers
82 views

Newton's Third Law Exceptions?

Lately I've been brushing up on some of my old Physics texts from college. Most recently, I've been rereading parts of "Classical Dynamics of Particles and Systems (5th ed.)" by Thornton and Marion. ...
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29 views

Coefficient of Static friction [on hold]

Kindly provide the reasoning for the direction of friction chosen...
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36 views

Vectors in three dimensions [on hold]

A plane travels 40 degrees east of north from the Heliport travelling horizontally distance of 2km while reaching an altitude of 2500m and turns travels horizontally another 3km and loosing 1500m in ...
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1answer
87 views

Why is the gravitational field potential scalar?

On page 48 of Carroll's Spacetime and Geometry he, before introducing "gravity as geometry", discusses the classical Newtonian equation: $F_{g}=-m_{g} \nabla \Phi$ This equation is very straight ...
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60 views

Lagrangian mechanics is different form Newtonian? [duplicate]

I am a post graduate student and had completed my classical Mechanics with Newtonian mechanics to Hamiltonian mechanics. I have better understanding of Newtonian, Lagrangian and Hamiltonian. But I ...
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16 views

Difference between marginally stable and marginally bound orbits

I have some difficulty understanding what marginally stable and marginally bound orbits are. This is what I have understood: Stable orbits: Stable orbits occur when the 2nd derivative of effective ...
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7answers
164 views

Is it possible to cut harder material with a less hard material?

Is it possible to cut harder material with a less hard material - for example cut a steel rod with iron blade ?
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47 views

Showing the Hamiltonian of the $\alpha$ FPU is real

I am studying the $\alpha$ FPU chain which is a model of coupled oscillators with small non-linearity. For these systems, I derived the following Hamiltonian $H$ which is given by $$ H=\sum_{j=1}^{N} ...
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3answers
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Motion on a frictionless vertical sinusoidal track

Today during lesson, my mechanics teacher provided a diagram of a "bowl" of the following shape: The top left and the top right have the same height, and the top right part is horizontal. He ...
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1answer
38 views

Is a motor HP torque directly proportional to the increasing HP among identical motors?

Say you have three motors: Motor 1 = .10 HP with x torque, performing task A Motor 2 = 1 HP with y torque, performing task A Motor 3 = 10 HP with z torque, performing task A If the motors are the ...
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1answer
55 views

Equation of motion for system of springs

I need to find the equations of motion for the following system. If $x_1$ is $m_1$'s extension and $x_2$ is $m_2$'s, then, I feel like for $m_1$ we just need to consider $x_1$ giving $$m_1 a_1 = ...
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1answer
33 views

Sympletic transformation and Hamiltonian function

Let's say that $x:=(p,q)$ is a trajectory in phase space and $$x'(t) = J \nabla H(x(t))$$ are Hamilton's equation of motion. Now I transform $F: M \rightarrow N, x \mapsto y(x)$ diffeomorphic to some ...
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75 views

Is angular frequency dependent on time in damped harmonic motion?

I have a doubt regarding the angular frequency of a harmonic oscillator when there is damping involved. The frequency of the oscillation changes with time in the case of damping, but I haven't seen ...
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3answers
77 views

If a body is floating in a static fluid, then the volume of the displaced fluid equal to the volume of the inmerse part of the object (proof)

Suppose an arbitrary body is floating in a static fluid, either totally or partially immersed in it, then the volume of the displaced fluid equal to the volume of the immersed fraction of the object. ...
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44 views

Initial conditions in classical mechanics

In classical mechanics, specifying the initial coordinates and velocities of all particles uniquely determines the system's future; we do not need to specify accelerations or higher derivatives. Can ...
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25 views

What forces are involved to enable a rock to skip in water?

Does the surface tension matter or is it something else that is providing the upward force? Can someone explain the phenomenon to me physically?
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22 views

Optimal size of a windmill for a given windspeed

Here is the problem: Assume that you have some constant wind speed. I want to run a windmill but I need to decide how big a windmill I want. The size is characterized by the length of the blades, $r$. ...
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55 views

Liouville's theorem and preservation of topology

What might be a simple proof showing that the time evolution of the phase space volume can't lead to splitting off of the phase space volume? I don't know much about topology and stuff.
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43 views

Simplifying Friedmann's Equation

So we have one of Friedmann's equation: $$\rho_c = \frac{3H^2}{8\pi G}$$ Using This website, resources where gathered for specific times in the universe. The resources being the Hubble constant at ...
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65 views

Do waves accelerate?

Typically we think of acceleration as a particulate property but a previous question on this forum got me thinking. If we think of a wave increasing its velocity by increasing its energy/frequency ...
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58 views

Movement of a cylinder filled with water

Not long ago I was pretty bored at a dinner and I started playing with a water bottle that was not empty: I've been quite interested in its behavior when putted on its side and pushed: the bottle of ...
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24 views

Effect of an asymmetric weight distribution on a hack squat machine

In a hack squat machine (see figure above), does it matter if I put more washers on one side? May this asymmetry cause an asymmetry of my effort in performing this exercise? For example, if I put ...
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Any good resources for Lagrangian and Hamiltonian Dynamics?

I'm taking a course on Lagrangian and Hamiltonian Dynamics, and I would like to find a good book/resource with lots of practice questions and answers on either or both topics. So far at my university ...
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Blowing your own sail?

How it this possible? Even if the gif is fake, the Mythbusters did it and with a large sail it really moves forward. What is the explanation?
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23 views

Restricted three body problem

I have the restricted three body problem, which corresponds, to the equation $ \ddot a-2\dot b -a= \displaystyle\frac{\partial U}{\partial a} $ $ \ddot b +2 \dot a-b = \displaystyle\frac{\partial ...
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3answers
252 views

Does the variation of the Lagrangian satisfy the product rule and chain rule of the derivative?

I have seen wikipedia use the product rule and maybe the chain rule for the variation of the Langragin as follows: \begin{align} \dfrac{\delta [f(g(x,\dot{x}))h(x,\dot{x})] } {\delta x} = \left( ...
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25 views

Confusion regarding a method of writing constraint equations

I came across a method for writing the constraint equations known as "The Virtual Work Method".I am quoting the exact language of the text(well,not exactly the exact)- Consider the atwood machine ...
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55 views

Why is commutation relations the first step in quantization?

Why is commutation relations the first step in quantization?
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1answer
39 views

Why do we exclude the $(i,i)$ case when summing over internal forces?

In the majority of the literature and lectures I see when a system of particles is involved, I usually see the following expression (or similar) for the total force on particle $i$: $$\vec{F}_i = ...
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1answer
53 views

How a fan moves air? [duplicate]

How does a fan moves air towards you (I mean in 1 direction). Also propeller and fan have different shapes, does it mean they work different?
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1answer
64 views

Why can't angular momentum be used in flying vehicles?

If angular momentum (L) works like this animation from Wikipedia leads me to believe, why can't we put a large flywheel or several small ones on a chassis, all rotating counter-clockwise around ...
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23 views

Can a harmonic drive reducer/strain wave gear be used to gear up instead of down? [closed]

I wish to be able to gear up from a rotating bicycle hub with a revolutions per minute range of 150 to 850 to a ratio of 200:1. Can I do this by simply reversing the direction of a harmonic drive ...
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1answer
33 views

How to reconcile these two approximations?

I'm working on what should be a simple problem (Taylor Classical Mechanics problem 6.23. Not homework.), but I'm having a tough time reconciling the many ways it can be tackled. An aircraft whose ...
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1answer
61 views

Calculating coefficient of friction

Consider a body attached to a horizontal spring and resting on a surface, inclined at an angle $\theta$ from the ground. The spring constant is $k$. Initially the spring was kept in its ...
2
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1answer
87 views

Example of Hamilton's Principle to Systems with Constraints (Goldstein)

I'm currently studying Goldstein's Classical Mechanics book and I can't get my head around his reasoning in section 2.4. (Extending Hamilton's principle to systems with constraints). I'd like to ...
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1answer
36 views

How is force exerted on a wall equal to derivative of hamiltonian with respect to wall position?

I'm trying to understand a solution of a problem in Landau, Lifshitz "Quantum mechanis. Non-relativistic theory" in $\S22$ "The potential well": Determine the pressure exerted on the walls of a ...
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2answers
50 views

Does the superposition principle affect the space of quantum states?

I am confused about the set of quantum states. I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.) In quantum ...
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1answer
37 views

Integrals of Motion for s Degrees of Freedom

From Landau & Lifshitz, Classical Mechanics, the number of integrals of independent integrals of motion for a system of $s$ degrees of freedom is $2s-1$. I am considering a spherical pendulum in ...
32
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5answers
4k views

What are washers for? [closed]

When you attach a bolt to something using a nut, it is clear what the roles of the nut and bold are. The more you tighten the bolt the more secure your fastening. However, you are often also told ...
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2answers
89 views

Does one really need classical physics in order to understand quantum physics? [closed]

I want to start studying quantum mechanics, and then move to quantum field theory. I have a strong mathematical background, and I think this aspect of quantum physics won't be a problem to me. Though, ...
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0answers
20 views

Perfectly vertical spinning top [duplicate]

Consider a non-spinning top. If a top is perfectly vertical, and the interface between its base and the ground is perfectly flat, it should stay in (unstable) equilibrium. I.e. it does fall. What ...
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1answer
51 views

A pendulum's rope swings and strikes a peg [closed]

So I have this problem, as far as I can tell I solved it correctly, and it's not equal to any of my answer choices. The problem is: A rope of length $L$ is attached at one end to a ceiling and at ...
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2answers
39 views

What is the percentage of energy recovery in Kinetic Energy Recovery Systems(KERS) in cars?

Kinetic Energy Recovery Systems (KERS) use flywheels to recover energy from the kinetic motion of cars. They use a rotating flywheel that generates energy as it rotates- this generates the electric ...
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1answer
286 views

The natural metric of a phase space and the Lyapunov exponent

For me, it seems that there is no apparent metric on a phase space of a dynamical system. Of course one can naively define an Euclidean metric on it, but it seems that this metric has not much to do ...