LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 M.Sc. NOVEMBER 2013
... 06. Show that the Hamiltonian is constant of motion if it is not an explicit function of time. 07. Show that the generating function F3 = pQ generates an identity transformation with a negative sign. 08. Show that [py ,Lz] = px 09. What is Jacobi identity? 10. Define Hamilton’s principal function S ...
... 06. Show that the Hamiltonian is constant of motion if it is not an explicit function of time. 07. Show that the generating function F3 = pQ generates an identity transformation with a negative sign. 08. Show that [py ,Lz] = px 09. What is Jacobi identity? 10. Define Hamilton’s principal function S ...
Question A particle is projected vertically upward in a constant
... Question A particle is projected vertically upward in a constant gravitational field with an initial speed of v0 . Show that if there is a retarding force proportional to the square of the speed, the speed of the particle when it returns to its initial position is v0 vT q ...
... Question A particle is projected vertically upward in a constant gravitational field with an initial speed of v0 . Show that if there is a retarding force proportional to the square of the speed, the speed of the particle when it returns to its initial position is v0 vT q ...
Physics 111 - Lecture 6 Dynamics, Newton’s Laws (Summary)
... Every body continues in a state of rest or uniform velocity unless it is compelled to change that state by a net force acting upon it. • Inertia of an object is its tendency to maintain its present state of motion. Mass is a measure of Inertia. Newton’s Second Law of Motion Force is equal to mass ti ...
... Every body continues in a state of rest or uniform velocity unless it is compelled to change that state by a net force acting upon it. • Inertia of an object is its tendency to maintain its present state of motion. Mass is a measure of Inertia. Newton’s Second Law of Motion Force is equal to mass ti ...
Chapter 11 - SFA Physics
... 12.2 Newton’s Second Law of Motion If the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitude of the resultant and in the direction of this resultant force. ...
... 12.2 Newton’s Second Law of Motion If the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitude of the resultant and in the direction of this resultant force. ...
PHYS4330 Theoretical Mechanics HW #1 Due 6 Sept 2011
... and numerically determine the period as a function of the (dimensionless) variable ym ≡ xm /a. It is easiest to write the period T as a definite integral over one quarter of the period, and then multiply by four. Your computer can do the integral numerically. Make a plot of T versus ym and show that ...
... and numerically determine the period as a function of the (dimensionless) variable ym ≡ xm /a. It is easiest to write the period T as a definite integral over one quarter of the period, and then multiply by four. Your computer can do the integral numerically. Make a plot of T versus ym and show that ...
Classical central-force problem
In classical mechanics, the central-force problem is to determine the motion of a particle under the influence of a single central force. A central force is a force that points from the particle directly towards (or directly away from) a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center. In many important cases, the problem can be solved analytically, i.e., in terms of well-studied functions such as trigonometric functions.The solution of this problem is important to classical physics, since many naturally occurring forces are central. Examples include gravity and electromagnetism as described by Newton's law of universal gravitation and Coulomb's law, respectively. The problem is also important because some more complicated problems in classical physics (such as the two-body problem with forces along the line connecting the two bodies) can be reduced to a central-force problem. Finally, the solution to the central-force problem often makes a good initial approximation of the true motion, as in calculating the motion of the planets in the Solar System.