All Questions

Filter by
Sorted by
Tagged with
0
votes
2answers
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 ...
2
votes
2answers
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 ...
0
votes
1answer
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 ...
0
votes
0answers
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 ...
4
votes
1answer
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, $E$ ...
4
votes
1answer
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 $q$? ...
0
votes
1answer
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 ...
4
votes
1answer
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?
2
votes
2answers
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 ...
0
votes
1answer
144 views

Confusion about virtual displacement

From Goldstein: A virtual (infinitesimal) displacement of a system refers to a change in the configuration of the system as the result of any arbitrary infinitesimal change of the coordinates $\...
2
votes
1answer
77 views

Is there any special significance of force field in physics?

What is the formal definition of force field? Which is more fundamental force or field? Do field exist in nature (as force do i think as per section 12-1 of Feynman lecture volume 1, and page 8,9 of ...
2
votes
2answers
236 views

Defining generalized momentum in terms of kinetic energy versus a Lagrangian

Reputable authors (e.g., Bergmann, Wells, Susskind) define generalized momentum using the Lagrangian $L$ as $$p_{i}\equiv\frac{\partial L}{\partial\dot{q}^{i}}.\tag{1}$$ Joos and Freeman define ...
0
votes
0answers
69 views

Is there any consensus on what is meant by Lagrange's equations of the first kind?

Is there any consensus on what is meant by Lagrange's equations of the first kind? Joos and Freeman define them as follows: Coordinates are given in terms of a rectangular Cartesian coordinate ...
8
votes
2answers
342 views

Meaning of the word 'canonical' in physics

I often encounter the term canonical in my study of physics. What does it mean? There is canonical momentum, canonical transformations and I have even heard the phrase 'proving something more ...
2
votes
1answer
71 views

Definition of Galilean structure in Arnold's book?

I am reading Arnold's Mathematical Methods of Classical Mechanics. He quickly introduces the notion of Galilean structure. The universe is defined as the affine space $A^4$ and time is defined as a ...
2
votes
2answers
2k views

What does “degrees of freedom ” mean in classical mechanics?

The definition I come up with is 3M - N ...where N is the number of constraints. I assume M is the number of distinct points. In what context is it used ? According to Wiki it says "an ...
1
vote
0answers
29 views

What is the difference between a defining equation and a word definition? [closed]

For example, can we define kinetic energy as the product of 1/2mu^2 and also as the energy that an object has due to motion ? are these definitions equivalent ?
1
vote
1answer
201 views

Phase space in classical field theory

In Classical Mechanics, a system has configurations described by points of a configuration manifold $Q$. In that setting we define the phase space of the theory to be the cotangent bundle $M = T^\ast ...
4
votes
2answers
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?
0
votes
0answers
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?
1
vote
3answers
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?
2
votes
1answer
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 ...
0
votes
1answer
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?
4
votes
2answers
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 ...
0
votes
0answers
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 $f(\mathbf{r}_1, \mathbf{r}_2, \dots , t) = 0$. ...
-1
votes
1answer
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)?
1
vote
1answer
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 ...
5
votes
1answer
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)?
8
votes
2answers
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 ...
1
vote
1answer
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 ...
5
votes
2answers
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 ...
0
votes
1answer
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 ...
5
votes
4answers
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 ...
0
votes
4answers
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 ...
0
votes
1answer
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 ...
0
votes
1answer
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 ...
1
vote
2answers
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 ...
1
vote
2answers
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.)
3
votes
3answers
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, ...
2
votes
2answers
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 ...
4
votes
1answer
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 ...
7
votes
4answers
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{\...
1
vote
2answers
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?
7
votes
3answers
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 ...
3
votes
2answers
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 ...
1
vote
1answer
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.
3
votes
3answers
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 ...
2
votes
3answers
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 ...
4
votes
3answers
65k views

Difference b/w Kinetics & Kinematics w/concrete example

(I know whether I understand this or not doesn't matter much to my work & study but am just curious.) I still can't differentiate in my head kinetics and kinematics (similar thread is found but ...
2
votes
2answers
19k views

What is the exact definition of center of gravity?

I've come across many definitions. Is it 1) The point from which the weight of the body acts, i.e., the point at which if the entire mass of the body is assumed to be concentrated, the gravitational ...