# Questions tagged [constrained-dynamics]

A constraint is a condition on the variables of a dynamical problem that the variables (or the physical solution for them) must satisfy. Normally, it amounts to restrictions of such variables to a lower-dimensional hypersurface embedded in the higher-dimensional full space of (unconstrained) variables.

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### Rigid body constraint

While going through the rigid body constraint, I encountered the following statement: For two rigid bodies to remain in contact, the relative velocity of the contact points on both the bodies along ...
1 vote
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### Example of a system which has both rheonomic and conservative constraint?

Generally speaking, rheonomic constraints are dissipative, although there are exceptions. This was given in classical Mechanics by Rana and Joag So, I was wondering what are those exceptions. If ...
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### Conceptual doubt in existence of normal force in a constrained motion problem [closed]

I was solving a problem on Wedge-constrained motion. Given below is it's diagram. This system is released from rest. All surfaces are assumed to be frictionless and string is inextensible. I have ...
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### Conceptual doubt related to normal force in a two-block system kept on frictionless surface

I was solving this question in which we had to calculate the normal force between blocks $m_1$ and $m_2$ Here, two blocks of mass $m_1$ and $m_2$ are in contact on a frictionless surface, and a force ...
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### Wedge constrained motion problem [closed]

I was solving this question on wedge-constrained motion: Q)Acceleration of blocks A and C are 2a and 3a respectively. Find the acceleration of block B. My Approach: Below I'm attaching a diagram ...
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### 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 ...
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### Integrability of a constraint when $x$ and $y$ depend on $t$ [closed]

I'm working through problem 6 in chapter 1 in Goldstein's classical mechanics book. I've reduced it to asking, if $x$ and $y$ are coordinates and function of time $t$, whether the differential ...
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### Constrained Hamiltonian problems [closed]

What happens to the poisson bracket structure of Hamiltonian phase space if We have some constraints in $p$ and $q$. What physical aspects this structure represents?
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### Regarding varying the coefficients of constraints in the pre-extended Hamiltonian in Dirac method

consider the following variational principle: when we vary $p$ and $q$ independently to find the equations of motion, why aren't we explicitly varying the Coeff $u$ which are clearly functions of $p$ ...
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### Analyzing uniform circular motion with Lagrangian mechanics

Consider swinging a ball around a center via uniform circular motion. The centripetal acceleration is provided by the tension of a rope. Now, is this force a constraint force? If it is, since it is ...
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### Constraint Force and Lagrangian multiplier

I can't seem to find my mistake in this problem and I think it stems from not understanding how to correctly form constraints and the meaning behind the Lagrangian multiplier. So first of all I ...
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### Setting constraints to zero in extended Hamiltonian

I am dealing with a system that has some secondary constraints. I am trying to use Dirac-Bergmann procedure by following chapter 10 of Ashok Das, Lectures on Quantum Field Theory ( 2021, Second ...
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### Counting degrees of freedom in theories with two-forms [duplicate]

I am reading Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics. I am thinking that I can apply the same arguments to the case of a two form, whose components are ...
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### Why impose constraints in (Path Integral) Quantization of Proca action?

I was reading the Wikipedia page on Proca Action. To summarize, it is almost like Maxwell action, but with a mass term because of which Proca action does NOT have gauge invariance. From the equation ...
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My question is whether there is any known method, which doesn't use calculus, to find the speed of ball C, given that the speeds of balls A and B are given at a certain moment in time. Suppose that in ...
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### Trouble with Lagrangian and Newtonian mechanics [closed]

I'm a pure mathematician and I was doing some physics for fun. I was trying to obtain the equations of motion of a particle moving along a curve $y(x)$ under the effect of gravitational force which ...
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### Discrepancy in Maxwell's extended Hamiltonian

In the 4D Maxwell's extended Hamiltonian action, I obtain the same expression of Fuentealba, Henneaux and Troessaert (see the picture), up to the term "$\partial^i\pi^0 A_i$", although my ...
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I'm learning about the field theory of electromagnetism. The Lagrangian density for an electromagnetic field can be taken to be $$\mathcal{L} = -\frac{1}{4} F^{\mu\nu} F_{\mu\nu} + \mu_0 A^\mu J_\mu ... • 853 1 vote 1 answer 164 views ### The problem of time in classical general relativity It is well known that the Hamiltonian of General Relativity is a linear combination of constraints. This poses a challenge in quantum gravity. If a state \psi solves the constraints (\hat C_\alpha \... • 155 1 vote 0 answers 53 views ### Constrained Lagrangian simulation. Fails depending on constraint definition [closed] Introduction I want to simulate a robotic leg that has a closed kinematic chain. The analytical equation i derived are compared with a simulink multibody model. Initially, my simulation failed, and ... 2 votes 1 answer 44 views ### Equivalent Characterizations of Rigid Bodies & Angular Velocity Interpretation In rotational kinematics, there seem to be two common characterizations of a rigid body: A rigid body is any collection of particles with position vectors \textbf x_1,\textbf x_2,... such that the ... 15 votes 1 answer 355 views ### What is the full algebra of BRST-invariant observables for general relativity? The Hamiltonian formulation of general relativity - either in the ADM formalism or in Ashtekar variables - is straightforwardly a gauge theory. While the BRST formalism has primarily been developed to ... • 127k 0 votes 0 answers 108 views ### Euler-Lagrange equations with constraints Show that if there are M independent constraints \phi_m(x_\mu,p_\mu) there are M of the \ddot{x}_i's that the Euler-Lagrange equations cannot be solved for. Attempt of solution: Assume that ... • 357 1 vote 1 answer 53 views ### When to consider constraint-equations and when not? Below is a first FBD from Robotics And Automation Handbook by T.R. Kurfess. The equations of motion for the system are constructed by using Kane's equations. That is, generalized coordinates q_1 and ... • 133 9 votes 1 answer 582 views ### Constraints Generating Gauge Transformations and BRST Given a gauge-invariant point particle action with first class primary constraints \phi_a of the form ([1], eq. (2.36))$$S = \int d \tau[p_I \dot{q}^I - u^a \phi_a]\tag{1} we know immediately, ...
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I have some problems understanding the transition from the Lagrangian to Hamiltonian formalism of electrodynamics. I will use the metric $(-+++)$. I want to start from the Lagrangian which is ...
I'm studying this paper on supersymmetric ground state wavefunctions. In section 5 "quantum mechanical gauge theories", it says: "We begin with the ${\cal N} = 2$ gauge theory which ...