# All Questions

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86 views

### What is a Hamiltonian of a System?

What is a Hamiltonian of a System? When learning about Hamiltonian for first time it is an object introduced as Legendre Dual Transform of Lagrangian of the same system. And we learn further that it ...
75 views

### In which sense equations of motion are covariant?

I read lots questions about what covariance is and I found out that, according to this topic Lorentz invariance of the Minkowski metric, we say an object is covariant if it doesn't take the same value ...
44 views

### Is this understanding of potential energy correct?

I am studying basic mechanics and have reached the chapter on potential energy. However I am a bit confused about the difference between potential energy and the formula for the potential energy due ...
21 views

### Inertial frame definition in Rindler Introduction to STR vs Landau' & Lifshitz Mechanics

Juxtaposing Rindler's Introduction to STR (page 7) vs Landau's Mechanics (page 5) inertial frame definition,I get that rindler assumes frame moving uniformly w.r.t inertial frame as an inertial frame ...
173 views

### Understanding pressure of gas in thermodynamics using 2D model

I am trying to understand why the pressure for adiabatic process is given for an ideal gas as the following. $$p = - \frac{\partial E}{\partial V} (V, X_1, ..., X_k)$$ where $p$ is pressure, $E$ ...
62 views

### Why is the kinetic energy a fixpoint of the Legendre transformation?

Question: Why is (from an intuitive standpoint) the kinetic energy $T$ a fixpoint of the Legendre transformation, i.e. $\frac{\partial T}{\partial \dot q}\dot q-T = T$ for any general coordinate $q$? ...
33 views

### Difference between kinematic momentum and conjugated momentum in purely mechanical setup

I don't know much about physics, but I wanted to understand what was the difference between the "kinematic momentum" and the conjugated momentum. As I understand it, kinematic momentum is mass times ...
68 views

### What is the difference between Non-Conservative and Dissipative?

We often hear these terms. However, they are often confused to be synonyms, but they are not. What are the rigorous definitions of them?
105 views

### How is mass defined by special relativity?

I am eagerly interested in all kinds of areas of physics. As the question of mass has been around for a pretty long time, I am interested about what modern physics namely special relativity says about ...
144 views

238 views

### What is the difference between tangent space and configuration space?

I am doing Lagrangian mechanics and working with Noether's theorem. Please, could you explain the difference between the configuration space and the tangent space?
282 views

### What is an orthogonal point transformation?

It is regarding classical mechanics. I know that a point transformation is the transformation of generalized coordinates. But what is meant by "orthogonal" point transformations?
996 views

### Phase space in classical mechanics

I am new in classical physics and I frequently come across the terms phase space and phase trajectory. Can anyone please explain to me what they are in a simple language?
1k views

### Situation of Stable, Neutral and Unstable Equilibrium

Recently, I was reading about stability of equilibrium. I came across the definitions for different types of equilibrium. Neutral Equilibrium: The kind of equilibrium of a body so placed that when ...
403 views

### A question about central forces

Will a force pointing towards a fixed point but having constant magnitude (and not depending on the distance from fixed point) be a central force?
796 views

### Are gravitational quadrupole moment, second moment of mass, and moment of inertia the same?

my understanding of moments is that they refer to distributions about an expected value, which allows us to make the multipole expansion. I read that: the zeroth moment of mass refers to the mass of ...
47 views

### Confused about the definition of holonomic constraints [duplicate]

I'm reading Goldstein's Classical Mechanics and he defines a constraint on particles having radii $\mathbf{r}_i$ to be holonomic if it can be written as $f(\mathbf{r}_1, \mathbf{r}_2, \dots , t) = 0$. ...
154 views

### Question About Momentum $p=mv$? [closed]

How Can We Derive the Momentum $p=mv$ Equation. Is there Any Mathematical Proof To Solve this Equation Directly. Or we can Said Momentum(p)=Mass(m)×Velocity(v)?
568 views

### Definition of the words “macroscopic/classical object” vs “quantum object”

Let's take the Schrodinger's cat as an example. In what sense is the cat different from the isotope ? We say that the isotope is "microscopic/quantum" and the cat is "macroscopic/classical" object ...
2k views

### What is the difference between kinetic momentum $p=mv$ and canonical momentum?

What is the difference, if any, between kinetic momentum $p=mv$ and canonical momentum? Why is canonical momentum important (specifically to classical field theory)?
5k views

### Understanding terms Twist and Wrench

In kinematics, physics and especially robotics, we often encounter the terms Twist and Wrench. Twist is (LinearVelocity, AngularVelocity) and Wrench is (Force, Torque). The reason I'm confused is I ...
190 views

### Possibility of defining “Path-dependent” potentials

Yes, I know the title seems stupid since the most important property of potential is that it's actually path independent. But I have a point. I just want to know is it possible to define a function ...
4k views

### What is a potential well?

What exactly is a potential well physically? [I've read the linked Wiki article, but it doesn't answer my questions, such as, what does it mean for a particle to "move along a potential" and "roll ...
98 views

### Field independent definition of “Potential function”(Not Potential Energy)

I know what "Potential Energy" is: A function like $U(x)$ whose negative gradient is equal to the force $F(x)$ generating it: $$F(x)=-\nabla U(x).\tag{1}$$ But the definition of the "Potential ...
465 views

### Is “Field” a more fundamental quantity or “Force”(in classical mechancis)?

Consider an isolated system consisting of two particles. We can say the two particles are exerting gravitational forces to each other due to their masses. Also we can say each particle has a ...
636 views

### What is the rigorous quantitative definition of the concept of “Energy”? [closed]

First of all I acknowledge you that I posted this Question on many other forums and Q&A Websites. So don't be surprised if you found my question somewhere else. I bet when the experts saw the ...
94 views

### What does it mean to find an equation of motion, given vector functions that describe both the object's position and velocity?

I don't really understand how to approach a problem that asks to find the equation of motion. Intuitively, I would guess that an "equation of motion" is an equation where the particle's position is ...
114 views

### What's phase curve according to Arnold at Mathematical methods of classical mechanics?

While trying to cleaning rust I read Arnold's Mathematical methods of classical mechanics edition 2. I find its phase curve and phase space definitions a bit vague. Here is a snapshot of the ...
326 views

### Is this constraint holonomic or non-holonomic?

$$f(q,q^\prime, t) = 0, ~\mathrm df = \frac{\partial f}{\partial q}~\mathrm dq + \frac{\partial f}{\partial q^\prime}~\mathrm dq^\prime+ \frac{\partial f}{\partial t}~\mathrm dt = 0$$ I really want ...
469 views

### What is difference between variations of the work and virtual work?

I really want to know whether or not both equations are the same mathematically. I think that they are the same, I just want to be sure. (Reference: this website.)
6k views

### What are the definitions of translational, rotational and rolling motion?

What are the exact definitions of pure translational , pure rotational and rolling motion? I am a class 11th student ... I find it difficult to exactly make a distinction between translational, ...
312 views

### How mass is determined in dynamics?

Mass is one of the most core and complicated concepts in dynamics. I have tried many books but I still don't have a good idea of how the mass of any object is determined relative to another. In The ...
788 views

### Rigorous definition of degrees of freedom

According to this Wikipedia article, the definition of degrees of freedom is: The degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its ...
525 views

### Is there a fundamental reason not to define the work vice-versa

My question arises from something which has never been really clear: in continuum mechanics, why is strain energy defined as: W=\int_\Omega \underline{\underline{\sigma}}:\mathrm{d}\underline{\...
3k views

### Constraint and Applied forces

In D'Alembert principle forces are classified into constraint and applied forces? Is this classification different from internal-external forces?
10k views

### Explanation of homogeneity of space and time by giving examples?

while reading landau lifshitz i came across these three terms:- homogeneity of space. homogeneity of time. isotropy of time. it will be a great help for me if someone can explain it to me by giving ...
342 views

### Physics textbooks that distinguish between laws and definitions?

Often when I am learning physics I start to think about whether the laws I'm learning are mere definitions or experimentally determined, and usually the textbook does not make this clear. As Thomas ...
1k views

### Hamiltonian Flow Map

I'm reading this article and am struggling with some of the terminology. What is the flow map for a Hamiltonian system? I'm looking for a rigorous definition really! Many thanks in advance.
5k views

### Stationary Solutions

An unbelievably basic question, but it's something I've never been taught. Am I right in thinking that the following defines a stationary solution? Let $\phi$ be some dynamical variable satisfying a ...
8k views

### What is the difference between a bounded orbit and a closed orbit?

Goldstein's Classical Mechanics has a puzzling few sentences in his discussion of orbits. Referring to the case of orbit where the energy is low enough for the orbit to be bounded, he says :"This ...