Question

5. Consider the functional Jlſ(t), Þ(t)] = (Hğ,p,t) - à p) dt of the 2n independent functions qı(t),...,qn(t), pi(t),..., p

0 0
Add a comment Improve this question Transcribed image text
Answer #1

- labelling each of the possible keaths in configur- ation space with a barameter & the s- variation a can be enfressed as -. e dei venisher at limits to and this as all kathe have the came termined. Therefore, egreation @ becomes . et=0 Petting daspy ) dtzo. - Elstilijon) - 663/640) - Since p; and fi are independent variate the - variation sp; and Sai will also be indep

Add a comment
Know the answer?
Add Answer to:
5. Consider the functional Jlſ(t), Þ(t)] = " (Hğ,p,t) - à p) dt of the 2n...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • 7. Consider the functional J(y) = SỐ[r(t)? + g(t)y?] dt. Find the Hamiltonian H(t, y, p)...

    7. Consider the functional J(y) = SỐ[r(t)? + g(t)y?] dt. Find the Hamiltonian H(t, y, p) and find Hamilton's equations for the problem.

  • 5*. Consider all sequences (ai,. .., an) such that a, are nonnegative integers and a ai+ 2. Let P...

    5*. Consider all sequences (ai,. .., an) such that a, are nonnegative integers and a ai+ 2. Let P, n and Rn be the number of such sequences which start from 0, 1 and 2 respectively. (a) Compute P, Qn, Rn by writing down all such sequences for n 1,2,3. (b) Prove that P, Qn Rn satisfy the recurrence relations: (c) Translate the above equations into linear equations for the generating functions for P, Qn, Rn (d) Solve these equations...

  • Differentiating the Hamiltonian. Starting with H(t, q, Р) %3D р .qlt, q, P) — L(t, 9,...

    Differentiating the Hamiltonian. Starting with H(t, q, Р) %3D р .qlt, q, P) — L(t, 9, q(t, q, P)) Рiа: (t, q. P)| — L(t, q, q(t, q. p)) Li=1 show that dH (4.163) дt dt along extremals Differentiating the Hamiltonian. Starting with H(t, q, Р) %3D р .qlt, q, P) — L(t, 9, q(t, q, P)) Рiа: (t, q. P)| — L(t, q, q(t, q. p)) Li=1 show that dH (4.163) дt dt along extremals

  • 1. A particle of mass m moves in three dimensions, and has position r(t)-(x(t), y(t), z(t)) at ti...

    Mechanics. Need help with c) and d) 1. A particle of mass m moves in three dimensions, and has position r(t)-(x(t), y(t), z(t)) at time t. The particle has potential energy V(x, y, 2) so that its Lagrangian is given by where i d/dt, dy/dt, dz/dt (a) Writing q(q2.93)-(r, y, z) and denoting by p (p,P2, ps) their associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy) H(q,p)H(g1, 92,9q3,...

  • 2. Consider a mass m moving in R3 without friction. It is fasten tightly at one...

    2. Consider a mass m moving in R3 without friction. It is fasten tightly at one end of a string with length 1 and can swing in any direction. In fact, it moves on a sphere, a subspace of R3 1 0 φ g 2.1 Use the spherical coordinates (1,0,) to derive the Lagrangian L(0,0,0,0) = T-U, namely the difference of kinetic energy T and potential energy U. (Note r = 1 is fixed.) 2.2 Calculate the Euler-Lagrange equations, namely...

  • 5. Consider the signal x (t) = cos (2n . 500) + cos (2n . 1...

    5. Consider the signal x (t) = cos (2n . 500) + cos (2n . 1 500). Its spectrum X1c" consists of a pair of spectral lines at positive and negative frequencies. Use the MATLAB command fft to find and plot the signal's spectrum using various values of N.

  • Differential equations question. dp/dt = 0.3 (1-p/10) (p/10-2)p 1. (5 points) Consider the given population model,...

    Differential equations question. dp/dt = 0.3 (1-p/10) (p/10-2)p 1. (5 points) Consider the given population model, where P(t) is the population at time t A. For what values of P is the population in equilibrium? B. For what values of P is it increasing? C. For what values is it decreasing? : (i-T-YE -2) p dt120 her

  • Problem 6. Consider the n independent trails in Problem 5. Let On be the probability that...

    Problem 6. Consider the n independent trails in Problem 5. Let On be the probability that there is no three consecutive successes in n trails. (1). Show that limn+cQn = 0 (2). Show that Qn = (1 - pQn-1 + p(1 - pQn-2 + p (1 - p)Qn-3 for n 3 (Hint: condition on the first failure). Problem 5. Suppose we do n independent trails that each has a probability P E (0,1) to result in success. Let Pn be...

  • Question 1: (5 marks) Consider a two-species model for populations Ni and N2 follows as N1 (a -bN1 cN2) dt N2 (d -...

    Question 1: (5 marks) Consider a two-species model for populations Ni and N2 follows as N1 (a -bN1 cN2) dt N2 (d - eN2 - Ni) dt (a) What kind of interaction does this system of equations represent? (b) Show that the equations can be simplified to dn1 an n1 (1 d7 dn2 Bn2 (1n2-n1). dT mT into the system of equations and picking by substituting N = kn\, N2 = ln2 and t appropriate constants k, l and m...

  • 5. Consider the following concentration table 4 NH3(g) 0.30 mol 702(g) 0.80 mol 〈=> 2N,04(g) + 6...

    Please answer ALL parts OF LETTER F and show work/explain LETTER F 5. Consider the following concentration table 4 NH3(g) 0.30 mol 702(g) 0.80 mol 〈=> 2N,04(g) + 6H20(g) I (initial moles) C (change) E (equilibrium moles) a) What are the values for each of the v;? b) Show that Σ v, Xi-0. c) Fill in the concentration table in terms of 5, the extent of reaction. d) According to your concentration table what are the minimum and maximum values...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT