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Question 1

0votes

0answers

25views

Transforming Initial Cartesian Uncertainty into Delaunay Variables for Orbital Uncertainty Propagation [closed]

I am working on orbital uncertainty propagation where the initial uncertainty is given in Cartesian coordinates(𝑟,𝑣)(r,v), either as a covariance matrix or as bounded (non-statistical) ...

Zhangshu Cheng

11

asked15 hours ago

Question 2

5votes

2answers

361views

A (probably wrong) proof that the fundamental Poisson brackets are independent of the special choice of the canonical variables

In Wolfgang Nolting's book Theoretical Physics 2 - Analytical Mechanics, the following theorem is stated:While the formal definition of canonical trasformation is given only several pages later in ...

John Garez

51

askedyesterday

Question 3

0votes

1answer

96views

Using conserved quantities as variables in Mechanics

I am currently taking a course in theoretical (classical) Mechanics, where I have learned about the Darboux theorem. My professor has also mentioned one can "reduce the system by symmetry", ...

Lagrangiano

2,646

asked2 days ago

Question 4

1vote

1answer

128views

Constraints in Dirac's Lectures

Currently, I am reading section 3 of a 1950 lecture/paper (PDF) by Dirac, about general hamiltonians and dynamics in the formalism. He defines$$H= \mathfrak{H(q,p)},\tag{7}$$weakly (as in only holds ...

Physicstn

75

askedNov 13 at 22:03

Question 5

-2votes

2answers

94views

Why do “points” in phase space correspond to possible physical states of a system, rather than “lines”?

Why aren't “lines” the physical states of system, instead of “points”? In a simple harmonic oscillator, the motion of particles changes back and forth between kinetic and potential energy, but it ...

Kanokpon Arm

153

askedNov 13 at 9:00

Question 6

2votes

2answers

96views

Why is the Hénon–Heiles system chaotic?

I am studying chaotic systems and classical mechanics and I am looking at the example of the Hénon–Heiles system.As I understand by the Liouville–Arnold theorem, if a system of $n$-DOF has $n$ ...

User198

1,586

askedNov 11 at 18:49

Question 7

1vote

0answers

63views

Worldsheet ADM Formalism & Hamiltonian Path Integral

Consider the following bosonic NS-NS sector of closed string worldsheet action, having the following spacetime fields - metric tensor $G_{\mu\nu}(x)$ Kalb-Ramond Field $B_{\mu\nu}(x)$ and scalar ...

Daniel Vainshtein

632

askedNov 8 at 10:02

Question 8

1vote

1answer

163views

Poincaré recurrence theorem in an infinite phase space

Regarding the Poincaré recurrence theorem there where already a few questions asked about boundness.However, I was wondering whether the theorem could still, in some form, hold within a Hamiltonian ...

Johannes Dahlke

13

askedOct 31 at 5:27

Question 9

1vote

1answer

125views

Interpreting one-dimensional Newtonian mechanics using complex numbers? (via Hamiltonian mechanics)

Let the configuration space of a single "point particle" be the one-dimensional affine space $\mathbb{A}^1 \cong \mathbb{R}$, with a chosen linear coordinate chart identifying some ...

Chill2Macht

576

askedOct 25 at 3:01

Question 10

1vote

0answers

56views

Sufficiency and necessity of symplectic conditions for time dependent canonical transformation

I'm studying Goldstein's classical mechanics book. I'm currently reading section 9.4, in particular, reguarding symplectic formalism, the author first proves for restricted canonical transformations, ...

Luke__

735

askedOct 23 at 21:38

Question 11

2votes

0answers

48views

Invariants of the Kovalevskaya top and Lie groups

I read that the Kovalevskaya top has 4 invariants of motion:energy $H_K$Kovalevskaya invariant $ K=\xi _{+}\xi$angular momentum component in the $z$-direction $L_z$magnitude of the $n$-vector: ${\...

User198

1,586

askedOct 23 at 20:08

Question 12

3votes

1answer

178views

Application of Dirac brackets to Dirac fermions in a tetrad gravity background

I have been studying the Dirac equation in curved spacetime, with the Lagrangian$$L=\Psi^{\dagger} \gamma^{0}(i\gamma^{\mu} D_{\mu} -m) \Psi$$(I think, however, I have seen it without the $\Psi^{\...

Physicstn

75

askedOct 22 at 19:45

Question 13

0votes

0answers

129views

Hamiltonian for perturbed scalar field

I research cosmological perturbations in modified gravity so i need write Hamiltonian for perturbed scalar field, but in literature there is different ways to get it.Mukhanov consider 2 actions: for ...

Heckfy

3

askedOct 1 at 17:42

Question 14

1vote

1answer

155views

Why does the total differential include $q$ but not $t$ in Landau & Lifshitz’s treatment of the Hamiltonian formalism?

In Landau & Lifshitz, Classical Mechanics, §40 (Hamilton’s equations), p.132-133, it is said that when writing the total differential of the Lagrangian and of the Hamiltonian, one ignores the time ...

SwitchArio

135

askedSep 24 at 9:41

Question 15

4votes

3answers

193views

Are these two notions of "conserved angular momentum" in axially symmetric spacetimes the same?

In Schwarzschild and Kerr spacetimes, when one studies the problem of a test particle undergoing geodesic motion, the use of symmetries is crucial in showing integrability and in solving the dynamical ...

newtothis

729

askedSep 23 at 16:51

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Questions tagged [hamiltonian-formalism]

Transforming Initial Cartesian Uncertainty into Delaunay Variables for Orbital Uncertainty Propagation [closed]

A (probably wrong) proof that the fundamental Poisson brackets are independent of the special choice of the canonical variables

Using conserved quantities as variables in Mechanics

Constraints in Dirac's Lectures

Why do “points” in phase space correspond to possible physical states of a system, rather than “lines”?

Why is the Hénon–Heiles system chaotic?

Worldsheet ADM Formalism & Hamiltonian Path Integral

Poincaré recurrence theorem in an infinite phase space

Interpreting one-dimensional Newtonian mechanics using complex numbers? (via Hamiltonian mechanics)

Sufficiency and necessity of symplectic conditions for time dependent canonical transformation

Invariants of the Kovalevskaya top and Lie groups

Application of Dirac brackets to Dirac fermions in a tetrad gravity background

Hamiltonian for perturbed scalar field

Why does the total differential include $q$ but not $t$ in Landau & Lifshitz’s treatment of the Hamiltonian formalism?

Are these two notions of "conserved angular momentum" in axially symmetric spacetimes the same?

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