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What is Hamiltonian cycle?
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- What is hamiltonian equationconsider the following two cases.14:06 Done 5 In Lagrangian mechanics, the Lagrangian technique tells us that when dealing with particles or rigid bodies that can be treated as particles, the Lagrangian can be defined as: L = T-V where T is the kinetic energy of the particle, and V the potential energy of the particle. It is also advised to start with Cartesian coordinates when expressing the kinetic energy and potential energy components of the Lagrangian e.g. T = ¹½ m (x² + y² + 2²). To express the kinetic energy and potential energy in some other coordinate system requires a set of transformation equations. 3.1 Taking into consideration the information given above, show that the Lagrangian for a pendulum of length 1, mass m, free to with angular displacement 0- i.e. angle between the string and the perpendicular is given by: L=T-V=2²² +mg | Cos и 4G 15 un
- Suppose that in a parallel Universe the gravitational force between two point particles, instead of fallingwith the square of the distance, falls with the power 3/2. That is, the modulus of the attractive force between theparticles of masses m1 and m2 is given in this Universe by: (see image), where K is the universal constant. l) I know that the formula for the gravitational potentital energy is : -(GMm/r) Il) I know that the formula for the gravitational force is: GMm/r2 QUESTION: What's the formula for the gravitational potencial energy? Provide the answer explaining the question below Looking at the formulas, it seems that the only difference between the two formulas is the 'r2', so, if the the r2 in the force is r3/2, r should be r3/4, but, according to the resolution(see 2nd image) it is r1/2. Why? DISCLAIMER: Explain why "r" cannot be r3/4, even though it apparently matches with the formula. Also, explain if there's a way to get to the gravitational potential formula without…Derive the total energy (E) of a particle of mass m moving in a centripetal force field, based on its radial coordinates and derivatives. If this particle moves in a spiral orbit expressed by the equation "(@) = cơ² (c, real constant), use the energy relation you find to obtain the force F(r) that forms this orbit.A particle is moving on xy plane, with x=15sin(2t), and y = 20cos(2t) In what kind of orbit is this particle moving?
- Can a particle moving under an inverse square repulsive force trace a closed orbit? Explain in brief.Show the derivation of free-fall equation using calculus method: Vf=gtA particle of mass moves in 1 dimensional space with the following potential energy: (in figure) where U0 and alpha are positive, 1) What is the minimum velocity a particle must have to go from the origin to infinity? 2) What is the angular frequency w of the oscillations around the stable equilibrium point?
- Hamiltonian of a system is given by: Difference between KE and PE Sum of momentum and speed O The square root of momentum + speed Sum of KE and PESuppose we let the radius approach zero. What would happen to the self-potential energy?Calculate the gravitational potential energy of the interacting pair of the Earth and a 6 kg block sitting on the surface of the Earth. You would need to supply the absolute value of this result to move the block to a location very far from the Earth (actually, you would need to use even more energy than this due to the gravitational potential energy associated with the Sun-block interacting pair). Ugrav = X J