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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661 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 ...
0
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1answer
25 views

The directions of the frictional force acting on the cylinder while ascending and descending cylinder

A cylinder rolls up an inclined plane,reaches some height,and then rolls down without slipping throughout these motions.The directions of the frictional force acting on the cylinder (A)While ...
-2
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1answer
70 views

Competition Physics Book for High School Physics

I am currently a high school physics student who has recently started participating in some physics competitions. Although I have an alright understanding of the physics and mathematics and can ...
1
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2answers
273 views

Mechanics Landau Galilean Principle

I started reading Landau's Mechanics book and was having some trouble understanding the Galilean Relativity Principle. What does Landau mean by saying space to be homogenous and isotropic and time is ...
0
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1answer
21 views

Wear rate with sliding speed

I read so many research studying the effects of sliding speed on wear using pin on ring testing machine all of papers said: when the sliding speed increase the wear rate will increase because the true ...
1
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2answers
40 views

Lagrangian mechanics not relying on time or independent of time [closed]

If neither the potential energy nor kinetic energy depends on time, then Lagrangian is explicitly independent of time I find this statement a little bit odd because velocity is distance over time or ...
-1
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2answers
120 views

Physics behind seemingly-impossible “rice bowl suction” Guinness world record? [duplicate]

By pressing a rice bowl on his abdominal muscles, Zhang Xingquan was able to create enough suction to pull a 36.15 tonnes heavy train for 40 meters Source: Guinness world records website. How does ...
2
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1answer
112 views

Simplest Live Demonstration of Adiabatic Transport

I have to give a presentation on Berry phase. I would like to give the simplest live demonstration of adiabatic transport. If I move an object in a loop and return that object back into its original ...
1
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2answers
628 views

Too big to revolve like an atom? [closed]

At what point do objects naturally start revolving as a disk? From an atom, with which the electron revolves as a sphere, to a galaxy, that revolves in the same direction? I herd about rigid ...
0
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0answers
27 views

Newton's third law, weak and strong law of action and reaction [duplicate]

In the case of a system of moving charges forces between charges is obtained by Biot-Savart law. But it violates both action and reaction law. How can we prove that?
1
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1answer
59 views

Projectile question doubt [closed]

A hunter wants to shoot a monkey with an arrow by launching the arrow at a speed $v_0$ at a distance of $L$ from the base of a tree of height $H$ on which the monkey is sitting. Now on watching the ...
16
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11answers
10k views

Book about classical mechanics

I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical ...
-1
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4answers
94 views

Which makes for a better equivalent capacitor? In series or in parrallel? [closed]

I understand how capacitors in series and in parallel work. However, I am wondering if it makes a difference, in terms of making a better capacitor that can store more charge, would you connect them ...
1
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1answer
71 views

Tilting a table

Let us say we have a perfectly horizontal table which has a cube placed on top of it. Furthermore, the cube is hollow and the sides weight is negligible. Now, what is the maximum angle that I can tilt ...
12
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5answers
3k views

Classical limit of quantum mechanics

I have heard that one can recover classical mechanics from quantum mechanics in the limit the $\hbar$ goes to zero. How can this be done? (Ideally, I would love to see something like: as $\hbar$ ...
3
votes
0answers
45 views

How does the bowling computer know I'm right handed? [closed]

I went bowling the other day and after I rolled my first ball I was suprised it was written on the screen that I was "right-handed". How was that figured out? My first guess is that there is ...
0
votes
1answer
62 views

Why does most galaxies resemble a 2 dimensional plane? [duplicate]

Older galaxies mostly tend the revolve forming a disk. Why are the stars not revolving around the center of the galaxy like a sphere instead similar to electron in an atom?
3
votes
2answers
136 views

Stable Sides of Polygon Objects

I have a physics question for you. Let us say a polygon shaped object is stable on a side when the center of mass "falls" inside the base. Is it possible in 2D to build an object that is unstable on ...
-1
votes
1answer
43 views

Studying dynamic elasticity for finite deformations

this is not a question asking for help with a problem but one asking for help where to begin serious study of elasticity, particularly that applied to dynamic systems. Most textbooks about elasticity ...
2
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2answers
98 views

Can energy conservation be derived from Newton's Laws?

Can the idea of energy conservation be derived from Newtons's laws? From inspection of his laws you can vaguely discern a relationship but I want to know of you can manipulate his laws to prove it. ...
2
votes
2answers
119 views

All reference frame are inertial? Where is the flaw in reasoning?

This is my first post here. I have a line of thoughts which might be wrong but I couldn't find the error. Suppose we have a point mass subjected to an arbitrary force $F$. In the lab reference frame ...
1
vote
1answer
73 views

Ball spontaneously rolling down hill [duplicate]

I'm trying to remember a problem in classical mechanics involving a special surface that allows a ball to roll to the top and lose all it's momentum in finite time. This leads to some interesting ...
5
votes
3answers
2k views

Formula for implementing a simulated weighing scale

Background: I'm on the pledge drive committee for a non-profit group, and there is an issue that is always contentious within this group; thankfully the group is amicable, although competitive, about ...
0
votes
1answer
41 views

How to find the axis of rotation or location given the angular velocity?

Say I have the angular velocity vector of a body as a function of time. How can I determine the axis of rotation/location of the body? we have the equation: $\frac{d\vec{r}}{dt}=\vec{\omega}(t)\...
2
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0answers
47 views

Non-canonical transformation

I would like to know any method to transform a known non-canonical set of variables to a canonical set for a given system. The Lagrangian and Hamiltonian are known in the non-canonical variables. I ...
1
vote
1answer
46 views

Note and homework organization [closed]

I am currently in a mechanics class and have some trouble trying to figure out how I should structure my lecture notes and my homework. I recently began rewriting my notes after class but I am still ...
77
votes
8answers
9k views

Could a “living planet” alter its own trajectory only by changing its shape?

In Stanislaw Lem's novel Solaris the planet is able to correct its own trajectory by some unspecified means. Assuming its momentum and angular momentum is conserved (it doesn't eject or absorb any ...
8
votes
1answer
115 views

Experimental data for asymmetric Newton cradle

Using a "successive impact model" (as if each ball were seperated from the other ones), I produced the following animations: You can see any combination of balls with masses of 1 or 2 (left) or 1 ...
2
votes
1answer
3k views

Poisson brackets and angular momentum

I'm trying to find $[M_i, M_j]$ Poisson brackets. $$\{M_i, M_j\}=\sum_l \left(\frac{\partial M_i}{\partial q_l}\frac{\partial M_j}{\partial p_l}-\frac{\partial M_i}{\partial p_l}\frac{\partial M_j}{\...
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votes
2answers
23 views

Cinematics; Equation of movement

What's the difference using the fórmulas v=d/t , or a=v/t, instead of equations of motion? I dont get it.
0
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4answers
106 views

Question on the constraint force of a string

I would like to know if the following statement is true or false even if I expect that it is true. Notation: I will consider a string that has no mass and that can not be extended. Saying that a ...
3
votes
1answer
133 views

The difference between the forms of the Euler-Lagrange equations

I'm trying to learn Lagrangian mechanics and have been reading a lot of articles on it. But many of the articles write the equations in different ways, probably for different purposes. The Euler-...
0
votes
0answers
18 views

How can I measure the stability of a many body gravitational system?

Suppose I have an N body planetary system interacting via gravity. Suppose I know the positions and momenta at t=0. How do I know if this system is stable (indefinitely)? By stable I mean the ...
1
vote
1answer
124 views

Spherical phase space dynamics

I have a hamiltonian of the form $$H(\phi,z) = (1-z^2)\cos(2\phi) + \chi z^2$$ with position $\phi$ and conjugate momentum $z$. It has this form provided that $z \in [-1,1]$ and we have natural ...
0
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0answers
19 views

Euler-Lagrange equation no fixed endpoints

The usual way, to show the Euler-Lagrange equation is, to find the minimum of the Integral $$ I = \int_a^b L(q, \dot q, t) dt $$ and argue, that it must satisfy the following equation $$ \frac{d}{dt} \...
1
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1answer
165 views

Consistent method for finding direction of static friction

I am having trouble coming up with a consistent method of determining the direction of static friction. So far the best I have come up with is: it should oppose the relative acceleration the contact ...
0
votes
2answers
62 views

what is the physical meaning of area moment of inertia?

In our applied mechanics class, we studied about area moment of inertia. Our teacher only explained the mathematical relation of this term that is product of area and square of the perpendicular ...
5
votes
3answers
69 views

Salt in a pot of water [duplicate]

I noticed that when I throw salt into a cooking pot and then mix, the salt collects in the center. As salt is denser than water, I would have expected it to go towards the border of the pot, and not ...
5
votes
2answers
198 views

Why do we use orthogonal axes?

I have been asked several times that “why do we use orthogonal axes in coordinate systems?” and I was always replying that “because of simplicity”. But, today morning, someone asked me that question ...
1
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1answer
33 views

Electric Field under Time reversal

We know under time reversal electric field does not change direction. I am doubtful about it. Imagine an electric field parallel to x-axis (in positive x direction) and a charge moving parallel to ...
2
votes
0answers
210 views

To prove uniqueness of the rotation tensor associated with rotation of a rigid body

Suppose there are $N$ particles embedded in a rigid body which undergoes some random rotation such that: $$ \overline{\overline {R}}_{ij} \otimes \vec{a}_{ij} = \vec{b}_{ij}$$ where, $i$ and $j$...
2
votes
0answers
31 views

Is there a form of rigid body dynamics that uses unit quaternions instead of Euler angles?

I’d like to know specifically about an elegant way of deriving a second derivative of an orientation quaternion from a torque and a moment of inertia matrix, if one is available. The straight forward,...
-1
votes
3answers
101 views

Why does the period of a pendulum decrease in an accelerating frame? [duplicate]

If there is a simple pendulum in a non-accelerating frame with period $T_1$, it will have period $T_2 < T_1$ when placed in a frame accelerating perpendicularly to the direction of gravity. Why?
1
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2answers
58 views

Lagrangian of an effective potential

If there is a system, described by an Lagrangian $\mathcal{L}$ of the form $$\mathcal{L} = T-V = \frac{m}{2}\left(\dot{r}^2+r^2\dot{\phi}^2\right) + \frac{k}{r},\tag{1}$$ where $T$ is the kinetic ...
1
vote
2answers
44 views

Relation between field and Potential energy of a body

I have read that if a body is in a field and is 1. moved in a direction opposite to the direction of a field, its potential energy increases.But why does it increase? 2.Also, if we move the body in a ...
2
votes
1answer
48 views

Collision/Crumpling problem possible solution mistake

This question is from Physics for scientist and engineers , Ohanian . Two automobiles of 540 and 1400 kg collide head-on while moving at 80 kmh in opposite directions. After the collision the ...
3
votes
0answers
50 views

Integrals of motion for a free particle

I'm struggling to understand the argument on p. 13 in Landau and Lifshitz that for a system with $N$ degrees of freedom there must be $2N-1$ integrals of motion. In particular, I can't understand ...
5
votes
3answers
89 views

The $\dot{q}$ term in the Euler-Lagrange equation

The Euler-Lagrange equation is about the functional $$ \int_{t_1}^{t_2} L(q, \dot{q}, t ) dt . $$ From a mathematical point of view, a simpler functional might be $$ \int_{t_1}^{t_2} L(q, t ) ...
0
votes
1answer
52 views

Why is it exerted a torque from the wheel on the body?

I'm looking at papers about two wheeled balancing robots. But they all seem to have a torque acting from the wheel on the body. As seen in figure 7 bellow. $M_M$ is the torque in question. Even though ...
0
votes
2answers
35 views

Discrete form of deformation gradient from vectors with finite length

I am writing some code for a deformable mesh and need to calculate a local deformation gradient within the material by using the vectors connecting material points. I think the method of solving ...