Show that Hamilton's equations of motion can be written in terms of Poisson brackets as [dot{q}={q, H}_{mathrm{q},

Question:

Show that Hamilton's equations of motion can be written in terms of Poisson brackets as

\[\dot{q}=\{q, H\}_{\mathrm{q}, \mathrm{p}}, \quad \dot{p}=\{p, H\}_{\mathrm{q}, \mathrm{p}}\]

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

Authors: T. M. Helliwell, V. V. Sahakian

See More Books

Question Posted: Mar 21, 2024 12:01 AM

See More Questions

s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...
(a) Assume that f(t), in problem 4.9, is given by exp (t). Show that, in this case, (t) satisfies the Bessel equation of zero order, where = ( c /2) exp (t). Determine the two solutions of this...
Consider the motion of a charged particle in a spatially uniform magnetic field that varies slowly in time as compared to the particle cyclotron period. (a) Show that the equation of motion can be...
Solve each system. If a system is inconsistent or has dependent equations, say so. -5x + 2y = -4 6x + 3y = -6
In Problem 26-14, what is the value of the Herfindahl-Hirschman index?
When assets are received before they are earned, what type of an account is credited? As the amounts are earned, what type of account is credited? pg58
Howshould an importance-performance analysis be performed? What do the four quadrants in the importance-performance grid represent?
Twain Services offers leadership training for local companies. It employs three levels of seminar leaders, based on experience, education, and management level being targeted: guru, mentor, and...
Once a CPA has determined that accounts receivable have increased due to slow collections in a "tight money" environment, the CPA would be likely to: Multiple Choice Review the going concern...
A Hamiltonian has the form \[H=q_{1} p_{1}-q_{2} p_{2}+a q_{1}^{2}-b q_{2}^{2}\] where $a$ and $b$ are constants. (a) Using the method of Poisson brackets, show that \[f_{1} \equiv q_{1} q_{2}...
Prove the anticommutativity and distributivity of Poisson brackets by showing that (a) $\{A, B\}_{\mathrm{q}, \mathrm{p}}=-\{B, A\}_{\mathrm{q}, \mathrm{p}}$ (b) \(\{A, B+C\}_{\mathrm{q},...
S&A Electronics sold a stereo set during a sale for $576. Determine the regular selling price of the set if the price of the set had been reduced by one-third of the original regular selling price....
Question 1 Consider the function g (x) = x-6x+1. The discriminant is [Select] [Select] and therefore the graph has x-intercepts.
Han Wu Manufacturing uses a job order cost system and applies overhead to production on the basisof direct labour hours. On January 1, 2023, Job no, 50 was the only job in process. The costs incurred...
Mr. A Background Mr. A is a 42-year-old divorced man assessed at intake to a crisis intervention unit. He was brought to the facility by the local law enforcement agency after his father complained...
QUESTION 1 The bank reconciliation statement of Honshu Ltd for February 2020 is set out below: 1) Bank reconciliation statement on 29 February 2020: < DR Balance as per bank statement Add:...
what do you think is the most important thing that adults can do to facilitate physical and motor development? Why?
Describe the characteristics of the ladder investment strategy and compare them to the barbell investment strategy. Why should the barbell strategy outperform the ladder strategy in a stable or...
What are bounds and what do companies do with them?
A sample of propane (C 3 H 8 ) is placed in a closed vessel together with an amount of O 2 that is 2.15 times the amount needed to completely oxidize the propane to CO 2 and H 2 O at constant...
Propose a structure for a compound with molecular formula C 10 H 14 O that exhibits the following 1 H NMR spectrum. Proton NMR Chemical shift (ppm)
A van der Waals gas undergoes an isothermal reversible expansion under conditions such that z < 1. Is the work done more or less than if the gas followed the ideal gas law?
Deacon Company is a merchandising company that is preparing a budget for the three - month period ended June 3 0 th . The following information is available Deacon Company Balance Sheet March 3 1...
Mango Company applies overhead based on direct labor costs. For the current year, Mango Company estimated total overhead costs to be $460,000, and direct labor costs to be $230,000. Actual overhead...
Which of the following do we expect to be the horizon growth rate for a company (long term growth rate- say 30-50 years)? A) Inflation B) Industry Average C) Zero D) Market Beta

Show that Hamilton's equations of motion can be written in terms of Poisson brackets as [dot{q}={q, H}_{mathrm{q},

Question:

Step by Step Answer:

Modern Classical Mechanics

Students also viewed these Sciences questions