Purchase Solution

Hamiltonian Dynamics in an Engine

Not what you're looking for?

Ask Custom Question

The governor for an engine, consists of two balls, each of mass m, attached by light arms to sleeves on a rotating rod. The upper sleeve is fixed to the rod, and the lower one of mass M is free to move up and down. Assume the arms to be massless and the angular velocity w to be costant. Find the Lagrangian and Hamiltonian functions, and obtain Hamilton's equations of motion describing the system. Solve for the angle theta at which the arms would stop waving, and obtain the frequency of small oscillations about the steady value. shown in figure 5.5

Attachments
Purchase this Solution
Solution Summary

This solution looks at the flyball governor situation and calculates the angle theta at which the arms would stop waving as well as the frequency of the small oscillations about the steady value using concepts of equilibrium and oscillation frequency. All steps are shown with brief explanations.

Purchase this Solution
Free BrainMass Quizzes
Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

The Moon

Test your knowledge of moon phases and movement.

Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

Basic Physics

This quiz will test your knowledge about basic Physics.

View More Free Quizzes
Related BrainMass Solutions

  • Lagrangian and Hamiltonian dynamics of a particle

    99716 Lagrangian and Hamiltonian dynamics of a particle A particle of mass m moves in one dimension under the influence of a force: F(x, t) = (k/x^2)*e^(-t/T) Where k and T are positive constants.

  • Involving Hamiltonian Dynamics

    147048 Involving Hamiltonian Dynamics Involving Hamiltonian Dynamics problem 5.6 A mass m is suspended by a massless spring of spring constant k and unstretched length b.

  • Dynamics and Hamiltonians : Hamilton's Equations

    29684 Dynamics and Hamiltonians: Hamilton's Equations A dynamical system, with one degree of freedom has Hamiltonian (see attachment for equation) ?

  • Hamiltonian proofs

    The graph GxH is defined as P=GxH, where V(P)={(i,j): i in V(G) and j in V(H)}, E(P) is the edge set of P. ((i,j),(k,r)) is in P if and only if (j,r) is an edge of H and (i,k) is an edge in G.

  • Lagrangian of Particle Moving in Electromagnetic Field

    Find the value of the Hamiltonian as a function of time for an initial condition of the particle at rest at t=0 Please see the attachment.

  • Hamiltonian Spin

    507675 Hamiltonian Spin Please assist me in solving the following problems: Let's consider an ion (in an effective spin state corresponding to s = 1) at a crystal lattice site.

  • Fully connected graphs

    A Hamilton Circuit (HC) is a cyclic ordering of a set of nodes such that there is an edge connecting every pair of nodes in the graph in order. A fully connected graph always has a HC.

  • Proof of the variational principle

    181427 Show that the average of the Hamiltonian is an upper bound to the ground state energy. Show that the average of the Hamiltonian is an upper bound to the ground state energy.

  • The motion of spring when the length of string shortened

    The total energy is not conserved in this system because work is done on the system and we have However, From the above equation, we can find out the energy and the Hamiltonian are identical for k=0, and the energy is conserved only for k=0.

View More Related Solutions