For the motion of a projectile write the Lagrangian and the Hamiltonian functions in polar coordinates and by using the Hamilton’s equation find the equations of motion.

Q: A particle of mass m described by one generalized coordinate q moves under the influence of a…

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Q: Write down the Hamiltonian for a projectile and determine the Hamilton's equations of motion in…

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Q: A disk of mass m of radius R is mounted on a swivel joint L from the center of gravity as shown…

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Q: Asynchronous Activity Consider a particle of mass m moving freely in a conservative freely in a…

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Q: Consider a block of mass m on the end of a massless spring of spring constant k and equilibrium…

A: Since you have posted a question that has more than three subparts, we will solve the first three…

Q: F A loaded penguin sled with weight W rests on a plane inclined at an angle relative to the…

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Q: The Longrongion of 1D harmonic oscilator is, () - write Euler-Congronge equation of system? ").…

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Q: Question one: Two masses m, M are joined with a light string of length L over a pulley of radius R…

A: Let center of disk be the level of zero potential energy and y1: height of m below the center of…

Q: Employing the power expansion to the solution of the equation of motion, show that for a…

A: Belongs to quantum dynamics and time development in quantum mechanics.

Q: The Lagrangian in generalized coordinates 1 2 L(0, 4, 8, 4) = gm R cos(0) + − m R² (¿² sin² (0) +…

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Q: Consider a free real scalar field $(x„), where r, = r, y, z for u = 1,2,3 and r4 = ict, satisfying…

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Q: A particle of mass m oscillates in a vertical plane suspended by a massless string that goes through…

A: This is the problem with the simple pendulum with a variable length of the pendulum.  That is  of…

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: Problem 3 The Lagrangian of a particle in spherical coordinates is given by 1 L(r, 0, 6; 1, 0, 0) =…

A: Step 1:The Lagrangian given for a particle in spherical coordinates is given in question Step 2: The…

Q: Since the Hamiltonian is obtained using a Legendre transform from the Lagrangian, these two…

A: Lagrangian mechanics Hamiltonian mechanics One second order differential equation Two first…

Q: For the motion of a projectile write the Lagrangian and the Hamiltonian functions in polar…

A: The Lagrangian of a system is defined as:L=T-V………(1)where,T is the Kinetic energy.V is the Potential…

Q: Find the Hamiltonian and the equation of motion for a mass connected to a horizontal plane A with no…

A: To find the Hamiltonian and the equation of motion for a mass connected to a horizontal plane with…

Q: In the o field theory, the Lagrangian density is 1 Problem 1 -- 4! Find the equation of motion and…

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Q: Verify that Y1 and Y1' are eigenfunctions of the 3D Rigid Rotor Hamiltonian.

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Q: 1. For an one-dimensional harmonic oscillator, the Hamiltonian is given as p2 +kx?. 1 H 2m (1a)…

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Q: A material point of mass m moves in space under the influence of an astral field forces, known…

A: A material point of mass m moves in space under the influence of an astral field forces, known…

Q: A particle of mass m is forced to move on the inner surface of a smooth cone with side-peak angle α.…

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Q: The action of a system describes all of its possible trajectories in time, and it can be calculated…

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Q: The free space Lagrangian for a particle moving in 1D is L (x,x, t) = a) Show that pat = SL = ymv b)…

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Q: Question 3 If the Lagrange's function for mechanical system is L = ;k (é² + g²(sin 0)² ) + g cos e.…

A: The Lagrangian is  L=12kθ˙2+12kϕ˙2sin2θ-gcosθ

Q: Yo STANDART FORM [4+h+ m,r} + m>q} 0 M(q) = m [4,(m,r +m>q;) cos q1 a„m2 sinqi g(q) = l. m, ,I a,

A: In classical mechanics as we know the 2nd order differential equation having a perticular stationary…

Q: Q2. A particle of mass m moves in a cylindrical symmetric force field given by k F(r,4,z,t) =e-t/h…

A: The first thing that comes to mind when you see this type of question is that whether you can resume…

Q: Find the equation of motion and the Hamiltonian corresponding to the Lagrangian L * = {{@, 9)² =…

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Q: Given the Hamiltonian H = p²/2m + a · p + V, with a = a(r) and V = the corresponding Lagrangian. If…

A: Here given that, Hamiltonian is H=p22m+a.p+V......................1Legrangian is the Logendre…

Q: 4. A particle of mass m moves in a central field of attractive force that has a magnitude () eat,…

A: Since given that Hamiltonian is time dependent then then energy is not conserved.

Q: Q2. For a simple pendulum of length t, the angle Obetween rest position and deflected position is…

A: We are given kinetic energy T and potential energy V of the system.

Q: Robot dynamic model in vector formats y dc2 Pc2 1. M(q)ä+ c(q, à) + g(q) = u dei 92 Cx(q, q) =…

A: As we know in classical mechanics the second order differential equation which are having sationary…

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Q: A projectile is projected at an angle 0 degrees above a horizontal surface with a velocity v, from…

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Q: Please provide a written answer

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Q: The series circuit in the figure is similar to arrangements that are sometimes used in radio tuning…

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Q: Two blocks with respective masses m,=2m and m,=m are connected through a light string over a…

A: Given: m1=2m m2=m Moment of inertia of pulley I=mr2 Angle of inclination   Let The distance of m1…

Q: Assume that you do not know about the kinetic energy or Newton’s Laws of motion. Suppose instead of…

A: Given data, There is a free particle, which is moving in the free space.