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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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 ...
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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?
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1answer
58 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 ...
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2answers
119 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 ...
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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 ...
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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 ...
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2answers
627 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 ...
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1answer
61 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?
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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 ...
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4answers
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What is momentum really?

Wikipedia defines momentum as in classical mechanics: In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object. However, an ...
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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. ...
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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 ...
2
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1answer
86 views

On the Stability of Circular Orbits

Bertrand's Theorem characterizes the force laws that govern stable circular orbits. It states that the only force laws permissible are the Hooke's Potential and Inverse Square Law. The proof of the ...
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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 ...
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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
46 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 ...
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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.
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1answer
130 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-...
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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 ...
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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} \...
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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 ...
8
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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 ...
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2answers
60 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 ...
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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 ...
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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 ...
5
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2answers
197 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 ...
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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 ...
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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,...
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3answers
98 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?
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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 ...
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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 ...
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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 ...
5
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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 ) ...
2
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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 ...
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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 ...
1
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1answer
75 views

Understanding Newton's Laws of Motion

I'm having difficulty understand Newton's laws of motion in practice, and how to model true dynamic systems. There are two examples below, where I cannot quite figure out what the true forces and ...
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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 ...
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0answers
57 views

Acclerated Coordinate Systems: Motion on the surface of the Earth (Fetter and Walecka)

So I am STRUGGLING, absolutely STRUGGLING to understand an example in my textbook. That's how bad I am, I can't even figure out how to do the example in my textbook. Anyway, I'm reading "Theoretical ...
2
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1answer
76 views

Relationship between zero modes and symmetry in a simple system of coupled springs

This Wikipedia page states that "zero modes appear whenever a physical system possesses a certain symmetry," and gives the example of a ring of beads connected by springs having a zero mode associated ...
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0answers
42 views

Reason behind $L = T - V$ (Lagrangian formalism) [duplicate]

I've been learning about the Lagrangian formulation recently, and while I'm with the process, I am still struggling somewhat with the theory behind it. As I (rather poorly) understand it, the ...
1
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1answer
127 views

When does a Trebuchet Shoot Its Projectile?

Consider the following sling trebuchet: While researching I found that what controls the release angle of the projectile is the angle between the 'finger' and the extension of the beam $r_b$, as ...
1
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1answer
49 views

Lagrangian in a system with a specific velocity dependent potential

I have a system of a particle moving under the generalized central potential $$ V= \frac{1}{r}(1+\dot{r}^2) \tag{1} $$ The general Euler-Lagrange equations for such type of potentials are: $$ \frac{...
6
votes
1answer
83 views

How does a lever magnify force? [duplicate]

I understand that energy is conserved when a force is applied to the end of a lever and magnified closer to the pivot point. However, I would like to know how it is the force is transferred and ...
1
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1answer
37 views

Homework exercise: a ball hits a rigid bar [closed]

I need a hand with the following exercise: A rigid bar of mass $M$ and length $L$ is hanging vertically from it's upper side, from which it can rotate freely. A particle of mass $m$ hits the ...
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0answers
28 views

Elastic Deformation coupled to simple oscillator

I have a system which I'm attempting to model as a spherical mass on a spring (cantilever) from above, and a somewhat elastic surface below. Are there any resources on how to model the resulting ...
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2answers
58 views

Rotating Frames of Reference: Doubt while deriving the velocity

I am following an online Chapter on Coriolis force, where the author develops the equations for a rotating frame of reference. The Figure and most of the notation used in the derivation can be ...
1
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1answer
50 views

Stability of the classical helium atom

Let us forget about quantum mechanics and confine ourselves to classical mechanics. The Hamiltonian for a classical helium atom would be $$ H = \frac{p_1^2 + p_2^2}{2m } - \frac{Z}{r_1} - \frac{Z}{...
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1answer
80 views

Solving 9 variable Normal Reaction equations of Sudoku board [closed]

We have a rigid Square board of negligible mass, which has been divided into a grid of 9 small squares(like a Sudoku Board), at centre of each square a point mass is attached. The gravity on the board ...
2
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2answers
79 views

Difference between naive and Coriolis-force calculation

Consider the classical problem of dropping a coin from a tower at the equator of a planet without atmosphere and with spin $\Omega$: where in relation to a plumb-line will the coin land? When doing ...
3
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3answers
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Mathematical Formulation of Classical Spacetime

I have seen two formulations of Classical Mechanics: Newtonian spacetime (learned it from the lectures of Professor Frederic P. Schuller): Definition: A Newtonian spacetime is a quintuple $(M, \...