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How to determine the nr. of degrees of freedom (for a system), for calculating the Lagrangian?

I want to have an understanding as what constitutes a degree of freedom of a system that we consider. My understanding of it, I believe, is pretty naive. I associate it with how an object moves in ...
imbAF's user avatar
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1 vote
2 answers
53 views

Degree of Freedom and Equations of Motion [duplicate]

I am a bit confused about the number of degrees of freedom of a simple pendulum. Is there only angular displacement, or angular displacement and angular velocity? Also, I am a bit confused on the ...
Ee Kin Chan's user avatar
1 vote
0 answers
60 views

About Yo-yo motion and forces constraint

The purpose of the Euler-Lagrange equation, is supposed to enable us to describe a system with the fewest possible coordinates, using generalized coordinates instead of traditional ones. However, in ...
Abdelhakim Benkrane's user avatar
1 vote
3 answers
84 views

Do we consider a spring to be a constraint in classical mechanics. If yes/no why so?

I was brushing up on my DOF concepts before moving on to Lagrangian mechanics. One of my professors told me that a spring is not considered a constraint but his explanation was not satisfactory in my ...
Harshitha Sridhar's user avatar
0 votes
0 answers
19 views

Precise Definition of Degrees of Freedom [duplicate]

I am taking Analytical Mechanics and while reading Goldstein's and LL something bothered me: can I say that a degree of freedom is an independent (generalized) coordinate? What bothers me is that we ...
user avatar
0 votes
0 answers
221 views

How many degrees of freedom does a diatomic and triatomic molecule have at high temperatures?

I understand that a diatomic molecule has 3 translational and 2 rotational degrees of freedom. But since there is only 1 vibrational mode associated with a diatomic molecule and 1 vibrational mode is ...
Srijan Das's user avatar
0 votes
2 answers
204 views

Is the equation for degrees of freedom $f=3N-k$ valid for all cases?

Consider the example of a linear triatomic molecule. Now at low temperatures, where we can exclude vibration, quite clearly degrees of freedom, $f=5$, with 3 translational and 2 rotational degrees of ...
Srijan Das's user avatar
0 votes
2 answers
91 views

How did the number of unknowns change in the Dirac equation?

So I haven't seen this argument addressed in any textbook which makes me doubt it's legitimacy. Here goes: Since Newton's $F=ma$ is essentially a second-order differential equation. Any equation of ...
More Anonymous's user avatar
2 votes
0 answers
58 views

Degree of freedom and Grubler formula

I am attempting to apply the Grubler formula (which can be found here: https://learnmech.com/how-to-calculate-degree-of-freedom-of/) to determine the number of degree of freedom, but it does not seem ...
c.leblanc's user avatar
  • 197
5 votes
3 answers
857 views

Doubt in Arnold's "Mathematical Methods of Classical Mechanics", Chapter 2

My question is about Arnold's book "Mathematical Methods of Classical Mechanics", chapter 2, section B (pg. 16). He talks about systems with one degree of freedom, i.e. systems described by $...
algebroo's user avatar
  • 165
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1 answer
70 views

Elastic collisions and internal degrees of freedom

As I was considering elastic collisions today a question popped into my head. Do elastic collisions imply that there are no internal degrees of freedom in the colliding objects which couple ...
scmartin's user avatar
  • 183
0 votes
2 answers
217 views

Dynamics: why do physicists include derivatives like $\dot{\theta}$ in the state space for a system like a pendulum?

I come from statistics, so my experience with physics is spotty, especially on some simple stuff. I have been working on some applications related to control theory lately, and was looking at some ...
krishnab's user avatar
  • 181
0 votes
0 answers
73 views

How many DOF does this system have?

I saw the problem above and thought it would be fun to solve it using lagrangians. However, in order to do this, one has to know the DOF of the system. And this is where it gets confusing for me. ...
Tanamas's user avatar
  • 334
1 vote
1 answer
452 views

What is the degrees of freedom (Lagrange equation) of two connected spool rolling down two inclines?

I'm quite confused as to how to use the Lagrange equation [second type] in a system which features a spool rolling down an incline. I think this particular example is quite representative of what is ...
Captain Husayn Penguin's user avatar
0 votes
1 answer
899 views

Degrees of freedom for Constrained Motion

I'm starting to learn about Degrees of freedom, and the idea of 'constrained motion' seems strange to me, surely any particle with a predefined path is 'constrained' in its motion, We also had ...
user1007028's user avatar
0 votes
1 answer
1k views

How much degree of freedom of a rigid body in $N$-dimensional space?

Well I have the answer it is $\frac{N(N+1)}{2}$ but what the procedure to derive it . I tried this. 1).I have $N$ number of translation freedom. To calculate the number of rotational freedom I tried ...
LEO PHYSICS's user avatar
4 votes
1 answer
453 views

Why are $p$ and $q$ independent variables in Hamiltonian formalism?

Let's say we have $(q, \dot{q})$ as the generalised coordinate and generalised velocity. If we have a Lagrangian given by $$L=Aq\dot{q}+Bq$$ where $A$ and $B$ are constants that give the right units ...
TaeNyFan's user avatar
  • 4,276
1 vote
3 answers
210 views

Why should degrees of freedom be independent?

To define the position of a system of $N$ particles in space, it is necessary to specify $N$ radius vectors, i.e. $3N$ co-ordinates. The number of independent quantities which must be specified in ...
user134613's user avatar
1 vote
0 answers
102 views

Representation of Holonomic Constraints by independent generalized coordinates

Say we have a system with N particles described by N position vectors: $\{\vec{r_{i}}\};$ $i=1,...N$ Say we have a holonomic constraint: $$f(\{\vec{r_{i}}\},t)=0 \tag{1}$$ Since we have one holonomic ...
user avatar
2 votes
0 answers
143 views

Understanding the Degrees of freedom of a Ballbot

A Ball Balancing Robot is dynamically stable robot capable of omnidirectional motion. It possesses non-holonomic properties and is a special case of underactuated system, classified as a Shape-...
欲しい未来's user avatar
4 votes
0 answers
297 views

Pendulum constrained by a spring and generalized forces [closed]

I've been going through some problem sets used in a classical mechanics course offered a few semesters ago as a way to prepare for when I have to take that course next semester and I've hit a snag ...
Tushnim Yuvaraj's user avatar
0 votes
2 answers
839 views

How to count degrees of freedom

I am able to visualize and see that $y=A \sin{x}$ has 1 degree of freedom, because $z=0$ and $y$ depends on $x$. However, its plot looks like a 2D plane, even though according to the DOF it is a 1D ...
Anshul Sharma's user avatar
1 vote
4 answers
1k views

What are the degrees of freedom of a dumbbell?

Edit 1: May be I should modify my question after getting the answers. I see why $(X_c, Y_c, Z_c, \theta, \phi)$ are legitimate Dof's of the dumb-bell, I never had any problem with that. Please ...
Anu3082's user avatar
  • 182
0 votes
1 answer
84 views

How do the degrees of freedom change

I came across the following problem in an old exam: How many degrees of freedom does a system of 4 mass points (A,B,C,D) have, if the distances AB, BC and CD are given? So my attempt was to say ...
user avatar
5 votes
1 answer
492 views

How can one modify the Nambu-Goto action to include the longitudinal degrees of motion?

The Nambu-Goto action is given by $$ S = -\frac{T_0}{c} \int_{-\infty}^{+\infty} d\tau \int_{0}^{\sigma} d\sigma \sqrt{ \Bigg(\frac{\partial X^\mu}{\partial \tau} \frac{\partial X_\mu}{\partial \...
jar-'s user avatar
  • 73
0 votes
1 answer
1k views

Independent coordinates of a rigid body

This is a quote from Classical mechanics by Goldstein: "To fix a point in a rigid body, it is not necessary to specify its distances to all other points in the body ; we need only state the ...
In the blind's user avatar
3 votes
2 answers
614 views

Understanding dependent/independent variables in physics

How does one determine the independent and dependent variables? What do the terms mean? Can they be derived from a formula? For example I saw in a textbook $F = k\Delta l$, Hooke's Law, that $F$ is ...
E C's user avatar
  • 148
3 votes
3 answers
2k views

Number degrees of freedom for Sphere on a inclined plane

How many generalized coordinates are required to describe the dynamics of a solid sphere is rolling without slipping on an inclined plane? What I think is that there two translational degrees of ...
Himanshu's user avatar
  • 12.1k
0 votes
2 answers
952 views

Number of degrees of freedom if independent coordinates are functions of time

If there are $n$ independent coordinates for a system of particles, but all of them are functions of time, is it correct to say that the degree of freedom is 1? If we know the instant of time we're ...
Shashank's user avatar
0 votes
2 answers
2k views

How to determine the number of generalized coordinates in the following example?

Question: In this exercise one needs to determine the generalised coordinates. We have a pendulum in a magnetic field $B$. The pendulum rotates around its axis with an angular velocity $ω$ on the ...
user avatar
2 votes
2 answers
464 views

How to determine the number of constraints in this problem set?

I don't understand how to determine the number of constraints in this given problem set in classical mechanics (picture attached down below). Now lets take a look at this problem for example where a ...
user avatar
1 vote
3 answers
241 views

Why not a $(q,\dot{q})$ space in Lagrangian Mechanics?

We know that the Lagrangian $\mathcal{L}(q,\dot{q},t)$ which is function of generalized co-ordinate, generalized velocity and time. We consider the dynamics of particle is in configuration space. But ...
Himanshu's user avatar
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0 votes
1 answer
1k views

Degrees of freedom for a bead on a parabolic wire?

How many degrees of freedom does a bead on a parabolic wire have? I think it must be two degrees of freedom since the bead is constrained to move on the wire (up, down motion and left/right motion). ...
dimes's user avatar
  • 75
0 votes
1 answer
757 views

How do you find the degrees of freedom of a rigid body moving parallel to a fixed plane surface? [closed]

Find the degrees of freedom of a rigid body moving parallel to a fixed plane surface. I know the definition of degrees of freedom which meant we need minimum number of coordinate to specify something....
Unknown's user avatar
  • 113
0 votes
0 answers
205 views

Generalized coordinates of two unequal masses attached to a mass-less rigid rod

Consider a system of two particles of masses $m_1$ and $m_2$ moving in a plane. Let the respective position vectors be $\mathbf{r_1}$ and $\mathbf{r_2}$. The particles are attached at the end of a ...
aneet kumar's user avatar
0 votes
1 answer
1k views

Lagrangian Mechanics - Bead sliding on a rotating rod

Say I have a bead of mass $m$ sliding on a friction-less rod (or wire) that is rotating with a permanent angular velocity $\omega$. The whole system is under the influence of a uniform gravitational ...
Michael's user avatar
  • 63
0 votes
0 answers
191 views

Difference between finite and infinitesimal motion

I am studying Arnold Sommerfeld mechanics. Here they talk about finite and infinitesimal motion. Quoted from the text: The simplest example of a non-holonomic condition is furnished by a sharp ...
user199996's user avatar
0 votes
0 answers
59 views

What are degrees of freedom in this context?

For translational motion, $$H_\text{trans} = \frac{p_x^2}{2m} + \frac{p_y^2}{2m} + \frac{p_z^2}{2m}$$ For rotational motion, $$H_\text{rot} = \frac{1}{2} \frac{L_x^2}{I_x} + \frac{1}{2} \frac{...
khaled014z's user avatar
0 votes
1 answer
54 views

How constraining are conservation laws and continuity principles?

Suppose there are $N$ particles with masses $m_1, m_2, ..., m_n$. Consider the $3N$-dimensional classical configuration space of such particles. Consider some arbitrary physically possible trajectory $...
Taro's user avatar
  • 255
2 votes
1 answer
2k views

Non-holonomic constraints, degree of freedom and generalized coordinates

If a system has $N$ coordinates and $M$ number of holonomic constraints then number of degree of freedom $=N-M$ and generalized coordinates $=N-M$ too. But if there are $k$ non-holonomic constraints ...
Barry's user avatar
  • 362
2 votes
0 answers
161 views

Rigorously define degrees of freedom

I want to understand if there is truly a rigorous definition for the degrees of freedom in a system. Say all of a system's physical states are contained in some set $S$. A seemingly acceptable (and I ...
Aakash Lakshmanan's user avatar
0 votes
0 answers
54 views

Degrees of freedom [duplicate]

Consider a system of 10 (say) point particles each at a fixed distance from each other in 3-D space. In this case, the number of degrees of freedom: $3*(number-of-particle)-\binom{10}{2}=3*10-45<0$ ...
D.Mason's user avatar
  • 25
-1 votes
3 answers
90 views

Constrained Curve in 3 Dimensions [closed]

I have a particle in a 3D space that moves on a curve of the function $$r(x)=\begin{bmatrix}x \\ x\sin(x) \\ \exp(x^2)\end{bmatrix}$$ I know that there must be 1 degree of freedom left thus $S = 3N-P$...
The Mastermage's user avatar
2 votes
1 answer
712 views

How to determine whether a set of coordinates are independent and sufficient to determine the system completely?

In Analytical mechanics, when we formulate our principles, in general, it is assumed that we start with a cartesian coordinate system, and then find some generalised coordinates $q_j$s they are all ...
Our's user avatar
  • 2,313
8 votes
4 answers
929 views

Question about holonomic constraints

Goldstein says that when a system of $N$ particles is subject to $k$ holonomic constraints, the positions $\mathbf{r}_1, \dots, \mathbf{r}_N$ can be parameterized by $3N - k$ independent coordinates $...
user avatar
1 vote
2 answers
88 views

Why the notion of degree of freedom is correct?

The intuitional definition for number of degrees of freedom is following: it is the minimal amount of numbers which allows us to describe the system's configuration correctly. For example, for dot ...
Alex Goldstein's user avatar
0 votes
0 answers
118 views

A problem on degree of freeedom?

[The problem is roughly] Toy “Supermag” makes it possible to construct, among others, polyhedrons — e.g. tetrahedrons, cubes, and many irregular polyhedrons, where the edges of the ...
Bijayan Ray's user avatar
0 votes
0 answers
40 views

What is degree of freedom in thermodynamics? [duplicate]

I have read a lit bit of degree of freedom in classical mechanics and hope to understand as if the number of variable used to describe a system in the configuration space. But in thermodynamics I read ...
Bijayan Ray's user avatar
0 votes
0 answers
68 views

What is the formal definition of Degree of Freedom? [duplicate]

Is the degree of freedom defined in classical mechanics same as the degree of freedom in thermodynamics? If not what is the formal definition of degree of freedom in thermodynamics?
Bijayan Ray's user avatar
3 votes
3 answers
5k views

Degree of freedom in Lagrange's formalism

Degrees of freedom $=3K-N$ where $K$ is number of particles and $N$ is number of constraints. How to find the number of degrees of freedom for a rigid body which has both translation and rotation, ...
MIT RAY's user avatar
  • 31