Consider a particle of mass of m which is constrained to move on the surface of a sphere of radius R. There are no external forces of any kind on the particle. How many generalised coordinates is required to describe this system? Construct the Lagrangian and obtain Lagrange's equations of motion for this system

Q: Question 5 * 5. A particle of mass m is projected upward with a velocity vo at an angle a to the…

A:

Q: Determine the Hamilton-Jacobi differential equation for the one dimensional motion of a particle of…

A: Given data, Potential of the particle :- V(x) = -bx

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

A:

Q: The Hamiltonian matrix has been constructed using an orthonormal basis: (1 1 0 2 2 1 2 0, 1 0 1 0 1…

A: Given, H^= H0^+V^=101210214+110022120And exact eigen values of H^λ1= 1λ2=7λ3=1

Q: In the figure opposite, particle A can move freely on a circular ring of radius R. Particle B is…

A: Solution attached in the photo

Q: 420 for a 2D 21 (;2 + 0 r² ) + Suppose that you have the Lagrangian L system in plane polar…

A: Lagrangian The Lagrangian of a system is a mathematical function that is a function of the…

Q: Find the langrangian for each of the following systems. Consider that the gravitational field is…

A:

Q: Use Lagrangian formalism to solve the following problem: A block of mass m is held motionless on a…

A: Given data: mass of block=m, mass of plane=M, the angle of inclination=θ, a) change in vertical…

Q: From the Lagrangian L(x,x)=-mx². -kx2 find the Lagrange's equation of motion: 2 2 Amx²+kx=0 OB.mx2.…

A: To write the Euler Lagrange equation of Lagrangian given above

Q: Which of the following statements is false? I. The reduced mass of a two-particle system is always…

A: Reduced mass:

Q: Obtain the equations of motion for the motion of a particle of mass m in a potential V(r,θ,ϕ) in…

A: The lagrangian of a particle is defined as L=T-VT is the kinetic energy of the particleV is the…

Q: Determine the motion expressions for each of the systems shown below by using the Euler-Lagrange…

A:

Q: Consider a bead of mass m on a circular wire of radius R. Assume a force kx acts on the bead, where…

A:

Q: Q 4 For the motion of a projectile write the Lagrangian and the Hamiltonian functions in polar…

A: Let m is the mass of object, then kinetic energy in terms of rectangular coordinate will be,…

Q: Determine the Lagrange Equation of Motion for the motion of a particle sliding down an inclined…

A:

Q: Q 2: A mass m is suspended by a massless spring of spring constant k and unstretched length b. The…

A: When a mass is suspended by a massless spring constant k and of length b then the kinetic energy…

Q: draw a diagram

A: To find the center of mass (CM) of a uniform solid hemisphere using spherical polar coordinates, we…

Q: A uniform cylinder of mass M sits on a fixed plane inclined at an angle .A string is tied to the…

A:

Q: A bead of mass M is threaded on the rod of length L. The rod rotates in the horizontal plane with…

A: A bead of mass M is threaded on the rod of length L. The rod rotates in the horizontal plane with…

Q: a. b. Determine the Lagrangian What is the equation of constraint?

A: To find :  Lagrangian equation of constraint

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: M m رے 0

A:

Q: A bead slides on the inner surface of a paraboloid z= C * r^4, as shown in Figure 2. C is a…

A:

Q: Consider a block and a wedge. The block (mass m) has no friction when it moves on the wedge (mass M)…

A: Given: The mass of the block is m. The mass of the block is M. The angle of inclination is α.…

Q: Find the equations of motion for the Lagrangian L = eγt(mq˙2/2 − kq2/2) How would you describe the…

A:

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

A:

Q: The system in the figure below consists of a massless spring with stiffness 60 N/m and unstretched…

A:

Q: Consider a particle of mass m with kinetic energy T = mx² moving in one dimension in a potential…

A:

Q: Some shape with mass m is connected on the end of string of length L and spinning with angular speed…

A: We can find answers to the above questions by identifying the forces acting on the mass. The details…

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: (1) Find the Lagrange function 2) Find the generalized forces of the constraint Qk (3) Find the…

A:

Q: Consider a bead of mass m sliding down a wire from the point P (xo, yo). %3D 1. Write and expression…

A:

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…

Q: Question Four: For the simple pendulum Shown: If the string is an elastic one with elastic (force…

A:

Q: DO NOT solve the problem.

A: According Given to the question  consider whole swimming pool as a control volume Given below you…

Q: Consider an Atwood's machine consisting of 2 masses m1 and m2. The 2 masses connected by a…

A: For the atwoods machine Derive Lagrange equation Equation for conjugate momenta

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

A:

Q: Please find the answer using [ijk] notation and matrices. At the very least find the inertia about…

A: The moment of inertia of a slender rod about an axis through one end perpendicular to the length of…