Consider a Hamiltonian of the form 0 U H = (5 %) + ^ ( 2 ) B with a value of << 1.
Q: For a one-dimensional system with the Hamiltonian H = p2/2 − 1 / (2 q2), show that there is a…
A: Given that,H=p22-12q2D= pq2-HtWe have Liouville's theorem which is,dFdt = ∂F∂t+F, HHere F = DSo in…
Q: imperfectly rough fixed A homogeneous sphere rolls down an sphere, starting from rest at the highest…
A:
Q: 7.40 *** The "spherical pendulum" is just a simple pendulum that is free to move in any sideways…
A:
Q: (c) The motion of a particle in a plane is governed by the Lagrangian (a² + ÿ²) + ¿(y& – xỷ). L =…
A:
Q: A ball moves freely on the surface of a round billiard table, and undergoes elastic reflections at…
A:
Q: Problem 3 (a) Consider a homogeneous cylinder of mass M, radius R and height h. Show that the…
A: Given Data:The masses of the cylinder and the cone are M and m respectively.The height of the…
Q: Prove that the relation ∂ri/∂qk =∂r˙i/∂q˙k holds if you have one particle system described by…
A:
Q: Consider the points A(−4, 2, 0), B(7,3,−2) and C(−2, −3,1) (a) Find a vector of length √6 in the…
A: Given points A(-4,2,0), B(7,3,-2) and C(-2,-3,1) AB→=7-(-4)i^+3-2j^+-2+0k^AB→=11i^+1j^-2k^…
Q: For motion in a plane with the Hamiltonian H = |p|n − a r−n, where p is the vector of the momenta…
A: Given: The Hamiltonian of the motion in a plane is The operator
Q: Q.n.3 A central force is defined to be a force that points radially, and whose magnitude depends on…
A:
Q: A particle of mass m slides under the gravity without friction along the parabolic path y = a x²…
A: Introduction: Lagrangian is a quantity that describes a physical system's state. Just the kinetic…
Q: The time-evolution of a physical system with one coordinate q is described by the La- grangian L = ?…
A: **as per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost…
Q: A particle of mass m is moving in a bowl. The profile of the bowl is rotationally symmetric, and in…
A: Given: The vertical distance of the particle in the bowl is the function of time t is z(t) = h(r(t))
Q: Find the mass of the lamina described by the inequalities x 20 and 7<y 37+V 49-x, given that its…
A:
Q: A small bead of mass m=1g moves without friction along the inner surface of a deep spherical cup,…
A:
Q: Consider a large solar sail in the form of a square with sides of length e = 100 m that is…
A: Light is nothing but excitation of the electric and the magnetic field in space. It also behaves as…
Q: Suppose the following three conditions are satisfied: (i) v1, v2, 03, w are linearly independent.…
A: Option b and c are the correct answer w→ is the scalar multiple of z→ Span v1→,v2→,v3→,w→, z→=span…
Q: Calculate with C: unit circle counter clockwise z2 dz (2z–1)2 (with residual theorem application)
A:
Q: Consider the Lagrangian for a bead on a rotating horizontal wire: L = m/2 ( ̇q2 + ω2q2). (a) What is…
A: The specified Lagrangian is: L=12mq˙2+ω2q2 Lagrangian field theory is a classical field theory…
Q: The force F acting on a particle constraincd to move along the x-axis is given by the fucntion F(x)…
A: The equilibrium condition is that the net force will be zero. that is, Fx=0
Q: Consider the spherical pendulum, which consists of a mass m suspended by a string from the ceiling.…
A:
Q: A particle of mass m is at rest on top of a smooth fixed sphere of radius a. Show that, if the…
A:
Q: If the kinetic energy T and the potential energy V of a mathematical system are given T = (k+;) i +…
A: The Lagrangian function is given by, L = T - V The Hamiltonian function is given by, Hq, p, t =…
Q: A bead of mass m slides on a long straight wire which makes an angle a with the upward vertical and…
A: Given a bead of mass m slides on a long straight wire which makes angle α with, and rotates with…
Step by step
Solved in 2 steps with 3 images
- Which of the following is the conserved quantity if the system having Lagrangian L= = m(x² + y²) – ² k(x² + y²). (a) Px (b) Py (c) L₂ (d) None(a) For one-dimensional motion of a particle of mass m acted upon by a force F(x), obtain the formal solution to the trajectory x(t) in the inverse form: m = ₂√ 2 {E – V(x)} where V (x) is the potential energy and x0 is the position at t = 0. (b) If the force, F(x) is a constant then what is the equation of the particles trajectory (x vs t). t(x): = dxObtain the inertia tensor of a system, consisting of four identical particles of mass m each, arranged on the vertices of a square of sides of length 2a, with the coordinates of the four particles given by (±a, ta, 0). Y m (-a,a) X (-a,-a). m O m (a,a) (a,-a)
- Express the Lagrangian for a free particle moving in a plane in a plane polar coordinates. From this proves that, in terms of radial and tangential components, the acceleration inpolar coordinates isa = (¨r − rθ˙2) er + (rθ¨ + 2 r˙ θ˙) eθ(where er and eθ are unit vectors in the positive radial and tangential directions).In a Hamiltonian system, what are the conditions for fixed points?A pendulum consists of a mass m suspended by a massless spring withunextended length b and spring constant k. The pendulum’s point of supportrises vertically with constant acceleration a. (a) Use the Lagrangian method to find the equations of motion. (b) Determine the Hamiltonian and Hamilton’s equations of motion.