Questions tagged [classical-mechanics]

Classical mechanics discusses the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces). If it's possible, USE MORE SPECIFIC TAGS like [newtonian-mechanics], [lagrangian-formalism], and [hamiltonian-formalism].

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, Special and General Relativity, Quantum Mechanics, and beyond. Rotational dynamics, Statistical Mechanics, and Fluid Mechanics are subsets of Classical Mechanics.

However, the broader term, , is often also used for and , as they also use the .

When to Use This Tag

Use when discussing general concepts of classical mechanics, i.e. the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces).

Use this tag only if , , , , , and the like are too specific. In general, you should not use together with or .

Overview

Classical mechanics is the study of the movement of bodies under the influence of forces. In the absence of either movement or forces, the subtopics and arise, whereas the ‘complete’ subject is often dubbed dynamics.

For point particles/bodies, there are three equivalent approaches to deriving the trajectories of said bodies: based on Newton’s Laws, based on the variational principle and following from Legendre transformations of Lagrangian mechanics.

More advanced subtopics are for the study of moving many-body fluids (liquids, gases), for the derivation of macroscopic laws from microscopic principles (often making use of the Hamiltonian formalism) and for the study of rotating solid bodies.

Textbooks

  • Structure and Interpretation of Classical Mechanics, by Sussman, Wisdom, Mayer.

  • Physics for Scientists and Engineers with Modern Physics, by Jewett, and Serway.

  • Classical Mechanics, by Goldstein, Poole and Safko.

  • Mechanics, by Landau and Lifshitz.

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What's the point of Hamiltonian mechanics?

I've just finished a Classical Mechanics course, and looking back on it some things are not quite clear. In the first half we covered the Lagrangian formalism, which I thought was pretty cool. I specially appreciated the freedom you have when…
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What makes a theory "Quantum"?

Say you cook up a model about a physical system. Such a model consists of, say, a system of differential equations. What criterion decides whether the model is classical or quantum-mechanical? None of the following criteria are valid: Partial…
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Calculus of variations -- how does it make sense to vary the position and the velocity independently?

In the calculus of variations, particularly Lagrangian mechanics, people often say we vary the position and the velocity independently. But velocity is the derivative of position, so how can you treat them as independent variables?
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Why the Principle of Least Action?

I'll be generous and say it might be reasonable to assume that nature would tend to minimize, or maybe even maximize, the integral over time of $T-V$. Okay, fine. You write down the action functional, require that it be a minimum (or maximum), and…
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Does a particle exert force on itself?

We all have elaborative discussion in physics about classical mechanics as well as interaction of particles through forces and certain laws which all particles obey. I want to ask, does a particle exert a force on itself? EDIT– Thanks for the…
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Toilet paper dilemma

There are two ways to orient the toilet paper: "over" (left image), "under" (right image). Each has it's pros and cons. For some reason, it's always easier to tear off the paper in the "over" orientation even though we apply the same force thus…
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Is Angular Momentum truly fundamental?

This may seem like a slightly trite question, but it is one that has long intrigued me. Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and generally rotational dynamics) can be fully derived…
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Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject and convince your students that in fact classical…
103
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Physical meaning of Legendre transformation

I would like to know the physical meaning of the Legendre transformation, if there is any? I've used it in thermodynamics and classical mechanics and it seemed only a change of coordinates?
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Why is a $5-60 mph$ time slower than a $0-60 mph$ time for some automobiles?

This doesn't make a lot of sense to me, from a physics 101 point of view. I've read a few blog entries on why this is, but none of them explain it well or are convincing. "something-something launch control. something-something computers." …
Paul C
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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 mass), would this be possible (in Newtonian…
Petr
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What is the difference between Newtonian and Lagrangian mechanics in a nutshell?

What is Lagrangian mechanics, and what's the difference compared to Newtonian mechanics? I'm a mathematician/computer scientist, not a physicist, so I'm kind of looking for something like the explanation of the Lagrangian formulation of mechanics…
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When is the Hamiltonian of a system not equal to its total energy?

I thought the Hamiltonian was always equal to the total energy of a system but have read that this isn't always true. Is there an example of this and does the Hamiltonian have a physical interpretation in such a case?
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Why does a system try to minimize its total energy?

Why does a system like to minimize its total energy? For example, the total energy of a $H_2$ molecule is smaller than the that of two two isolated hydrogen atoms and that is why two $H$ atoms try to form a covalent bond. According to the classical…
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Why does dry spaghetti break into three pieces as opposed to only two?

You can try it with your own uncooked spaghetti if you want; it almost always breaks into three when you snap it. I am asking for a good physical theory on why this is along with evidence to back it up. Or, a reference to a good study previously…
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