Homework Answers
Add Answer to:
Mechanics system is described by the following Lagrangian: where a, b, c, d are constants. Determine...
Lagrangian and Hamiltonian mechanics The Lagrangian for a particle with velocity i = y and electric...
Lagrangian and Hamiltonian mechanics
The Lagrangian for a particle with velocity i = y and electric charge q in an electromagnetic field with Coulomb potential o(i) and vector potential A(7,1)is: L= mü? -9(0-v. A) a) Show that the canonical momentum is: p=mü +GĀ. This is an example of the generalised momentum not being the Newtonian momentum. b) Show that the Hamiltonian corresponding to the Lagrangian, H = P.y-L, is the energy of the particle in the field defined by O...
14. The Lagrangian for a system can be written as <= ax + b3 + e*j + fy+si+g3 – W/22+y2, where a, b, c, f. 8, and...
14. The Lagrangian for a system can be written as <= ax + b3 + e*j + fy+si+g3 – W/22+y2, where a, b, c, f. 8, and k are constants. What is the Hamiltonian? What quantities are conserved?
Conservation of energy: Using Hamiltonian or Lagrangian Mechanics 2) A particle P, of mass m, is...
Conservation of energy: Using Hamiltonian or Lagrangian Mechanics 2) A particle P, of mass m, is attached by means of two light ideal springs (no damping) to fixed points A and B such that APB is a vertical straight line of length 5a. Spring AP is of stiffness k, spring PB is of stiffness 4k, and both springs are of natural length a. Point A is directly above B. i) Show that when the particle is in equilibrium AP =...
Determine the steady state of the following ODE system, where a and b are assumed constants...
Determine the steady state of the following ODE system, where a and b are assumed constants allowed in the solution: Please show all steps clearly. We were unable to transcribe this imageWe were unable to transcribe this image
4. The dynamics of a simple harmonic oscillator is described by a Lagrangian (a) Show that the La...
Question (b) and (c) ONLY.
Thanks.
4. The dynamics of a simple harmonic oscillator is described by a Lagrangian (a) Show that the Lagrangian changes with a full derivative, L' = L +X, consequently the action is invariant under the two-parameter transformation yA sin(t w) +Bcos(t )+x (b) Find the two independent constants of the motion associated with an infinitesimal version of the above transformation, and identify their physical meaning. (c) Use the results of (b) to write down the...
Langrange function of a dynamic system is given below, a, b, k1 and k2 are constants. ...
Langrange function of a dynamic system is given below, a, b,
k1 and k2 are constants.
a) Find
the Hamiltonian function of the system?
b) Determine
the Hamiltonian equations of motion for this system?
c) Find
conservative values, if any?
2 2 Х. L xi 2 a bx
2 2 Х. L xi 2 a bx
5. Consider the following time-dependent Lagrangian for a system with one degree of freedom , (10)...
5. Consider the following time-dependent Lagrangian for a system with one degree of freedom , (10) where 8, m and k are fixed real constants greater than zero. (total 10 points) (a) Write down the Euler-Lagrange equation of motion for this system, and interpret the resulting equation in terms of a known physical system. (1 point) (b) Find Hamiltonian via Legendre transformation. (1 point) (c) Show that q(t) and the corresponding canonical momentum p(t) can be found as follows for...
Lagrangian Mechanics: A pendulum of mass m and length l hangs from the rear view mirror...
Lagrangian Mechanics: A pendulum of mass m and length l hangs from the rear view mirror in a car traveling with horizontal acceleration a. Assume the car starts from rest at time t=0. (Solve using Lagrangian Mechanics.) a) Draw a diagram of the situation. Write out the x and y coordinates of the position of the pendulum in the in terms of the angle of the pendulum, Φ, and the time t. b) Write out T, U, and L in terms...
In the theory of relativity a particle of mass m and position moving in R3 is described by the Lagrangian t1 where the speed of light c is a constant and a dot denotes differentiation with respect...
In the theory of relativity a particle of mass m and position moving in R3 is described by the Lagrangian t1 where the speed of light c is a constant and a dot denotes differentiation with respect to time. Compute the equations of motion. Show that, if T is an anti-symmetric matrix, i.e. T =-TT, then verify that it is conserved. Compute the conjugate momentum p and energy E and verify that they are conserved. Show that Evaluate the energy...
Let's consider a function described in terms of its displacement y(x,t) at t 0 by: where a, b and e are positive constants a) Write an expression for this wave profile, having a speed in the nega...
Let's consider a function described in terms of its displacement y(x,t) at t 0 by: where a, b and e are positive constants a) Write an expression for this wave profile, having a speed in the negative x-direction, as a function of position and time (b) Sketch the profile of the wave at t-0 s and t 2 s if v1 m/s (c) Determine if the following functions describe a travelling wave: (i) vr,t) (ar+ bt c), where a, b...
Lagrangian and Hamiltonian mechanics
The Lagrangian for a particle with velocity i = y and electric charge q in an electromagnetic field with Coulomb potential o(i) and vector potential A(7,1)is: L= mü? -9(0-v. A) a) Show that the canonical momentum is: p=mü +GĀ. This is an example of the generalised momentum not being the Newtonian momentum. b) Show that the Hamiltonian corresponding to the Lagrangian, H = P.y-L, is the energy of the particle in the field defined by O...
14. The Lagrangian for a system can be written as <= ax + b3 + e*j + fy+si+g3 – W/22+y2, where a, b, c, f. 8, and k are constants. What is the Hamiltonian? What quantities are conserved?
Conservation of energy: Using Hamiltonian or Lagrangian Mechanics 2) A particle P, of mass m, is attached by means of two light ideal springs (no damping) to fixed points A and B such that APB is a vertical straight line of length 5a. Spring AP is of stiffness k, spring PB is of stiffness 4k, and both springs are of natural length a. Point A is directly above B. i) Show that when the particle is in equilibrium AP =...
Question (b) and (c) ONLY.
Thanks.
4. The dynamics of a simple harmonic oscillator is described by a Lagrangian (a) Show that the Lagrangian changes with a full derivative, L' = L +X, consequently the action is invariant under the two-parameter transformation yA sin(t w) +Bcos(t )+x (b) Find the two independent constants of the motion associated with an infinitesimal version of the above transformation, and identify their physical meaning. (c) Use the results of (b) to write down the...
Langrange function of a dynamic system is given below, a, b,
k1 and k2 are constants.
a) Find
the Hamiltonian function of the system?
b) Determine
the Hamiltonian equations of motion for this system?
c) Find
conservative values, if any?
2 2 Х. L xi 2 a bx
2 2 Х. L xi 2 a bx
5. Consider the following time-dependent Lagrangian for a system with one degree of freedom , (10) where 8, m and k are fixed real constants greater than zero. (total 10 points) (a) Write down the Euler-Lagrange equation of motion for this system, and interpret the resulting equation in terms of a known physical system. (1 point) (b) Find Hamiltonian via Legendre transformation. (1 point) (c) Show that q(t) and the corresponding canonical momentum p(t) can be found as follows for...
In the theory of relativity a particle of mass m and position moving in R3 is described by the Lagrangian t1 where the speed of light c is a constant and a dot denotes differentiation with respect to time. Compute the equations of motion. Show that, if T is an anti-symmetric matrix, i.e. T =-TT, then verify that it is conserved. Compute the conjugate momentum p and energy E and verify that they are conserved. Show that Evaluate the energy...
Let's consider a function described in terms of its displacement y(x,t) at t 0 by: where a, b and e are positive constants a) Write an expression for this wave profile, having a speed in the negative x-direction, as a function of position and time (b) Sketch the profile of the wave at t-0 s and t 2 s if v1 m/s (c) Determine if the following functions describe a travelling wave: (i) vr,t) (ar+ bt c), where a, b...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago