Analytical mechanics Definition and 67 Threads

Homework Statement A projectile is launched from a platform that is moving horizontally with velocity v=(v,0,0). The initial velocity of the projectile is u with a launch angle theta relative to the platform. (a) Show that the range of he projectile is R= u^2*sin(2*theta)/g + 2*v*u*sin(theta)...

Hello. Someone knows the book: "Analytical Mechanics: An Introduction" by Antonio Fasano, S. Marmi? Is this a good book on mechanics? Thank you.

This is stuff I do in order to understand analytical mechanics better, I encounter the followin thing: \frac{\partial L}{\partial \dot{\phi}} = \text{?} Where \dot{\phi} = \frac{\partial \phi}{\partial q} \frac{dq}{dt} = \frac{\partial \phi}{\partial q} \dot{q} I should know this! It is...

m equations of semi-holonomic constraints can be put in the form: fi=(q1,q2,...,qn,\dot{q}1,...,\dot{qn}) but "commonly appears in the restricted form: \Sigmaaikdqk +aitdt = 0 (i,k,t preceded by "a" should appear in subscript and the sum is over k) I don't understand this form. what are...

I am currently taking the second semester of a 2 semester course in Mechanics. We are using the book, Analytical Mechanics by Fowles and Cassiday. This book is okay, but I'd really like to find a used secondary mechanics book with more explanations and problems to solve. Can anyone recommend...

i am studing Analytical Mechanics in these days.it is really amazing. but a question pazzles me .it seems: to generalized coordinates q,δq is arbitrary,it can equal 0;while variation in the x-coordinate, δx is not. i just cann't understand

Homework Statement Consider a point mass m moving under the influence of the gravitational force F= -mg e_y . The mass is constrained to slide along a given curve y= f(x) in the x-y plane. You may set z=0 from the start and consider two dimensional motion. c) A Skier descends a slope with...

As in the attached picture. A cylindrical shell with mass M can roll without gliding on a horizontal plane In the cylindrical shell a particle ,p, with mass m can glide without friction. At the beginning there is no motion and the angle to the particles position is \phi=\frac{\pi}{2}...

Hi, I am looking for books which discuss Mechanics at the same level as "Analytical Mechanics" by Fowles & Cassiday. If you know of any can you please help. Thank you.

I am not quite sure how to start this problem: A bullet of mass m is fired from a gun of mass M. If the gun can recoil freely and the muzzle velocity of the bullet is v. Show that the actual velocity of the bullet relative to the ground is v/(1+b) and the recoil velocity from the gun is...

I'm stuck on this problem: The initial conditions for a two-dimensional isotropic oscillator are as follows: t=0, x=A, y=4A, v=0i +3wAj (vector) where w is the angular frequency. Find x and y as functions of t. Where do I even begin with this problem. I take it A = constant. Can anyone...

Thanks for integral, he made the potential.pdf analyse for an analytical mechanic but i still have 2 questions, 1- Why does the length up between the tengency point and top of (h) equals: \ell + r\theta ? 2- Why the kinetic energy here equals: T = \frac{1}{2} m(\ell + r\theta)^2...

Hi guyz, I taked the picture attached with my mobile directly from the book, please help me to find the weights of A,B (not masses), and the friction coefficient (f) for A on the Horizontel plane, and note, the rope isn't able to change lenght, System is static, A,B are equal, weight of K is Q...

Sorry for that title, but what can I say, I'm going to be mad to get the motion equation for some systems but always failing system 1: a rope rounded to a cylinder, the rope ends with a mass m and creating a pendulum with a maximum angle creating on a vibration \theta, the length of the...

hi i am writing you from turkey.i am a physics student.it is my 2.year.i have a lesson called analytical mechanics.i want to ask to other physics students that they have a lesson like this or not.if you have can you tell me how can i pass it.it is very hard...

If some dude jumps into the ocean from a 10m diving board so that when he makes contact with the water F=-mg + cv^2 where c is some frictional constant, how do I solve for the velocity of the guy as a function of the depth under water? I am able to integrate so that I obtain velocity as a...

I was wondering what people thought about the notion of creating a forum for analytical mechanics, i.e. Lagrangian and Hamiltonian dynamics. If not then what forum would you recommend discussing the subject? Thanks