ME201 Advanced Dynamics (Fall 2007) HW-5 Solution (100 pts) 1. 30 pts Consider the standard map studied in class. I = I + sin(2) = + I + sin(2) Study the change of the phase space of the standard map as changes from 0 to 2 . Specically, plot the cases of
ME201 Advanced Dynamics (Fall 2007) HW-3 Solution (100 pts) 1. 50pts Consider the following linear dynamical system on R2 : x = ax + by y = cx + dy In matrix form, this system can be written as x = Ax for a matrix A, where x = (x, y ). Find the matrix A.
ME201 Advanced Dynamics (Fall 2007) HW-2 Solution (100 pts) 1. 50pts Consider the system of two oscillating equal masses given by mx1 = kx1 + c1 (x1 x2 ) + c2 (x1 x2 )3 mx2 = kx2 c1 (x1 x2 ) c2 (x1 x2 )3
(a) Is this a conservative system? At rst, you may
ME201 Advanced Dynamics (Fall 2007) HW-1 Solutions (100 pts) 1. 20pts Write Newtons equations of motion for two particles of masses m1 and m2 interacting via Newtons law of gravitation. How many degrees of freedom does the system have? Without any further
MEE 201 Advanced Dynamics. 12/04/2007.
Homework set No. 6 Due Tuesday, 12/11/2007. 1. Consider the system shown in gure 1. Derive equations of motion using Lagrangian approach.
Figure 1: 2. Consider the system shown in gure 2. Derive equations of motion u
MEE 201 Advanced Dynamics. 11/15/2007.
Homework set No. 5 Due Wednesday, 11/22/2007 in class. 1. Consider the standard map studied in class. I = I + sin(2), = + I + sin(2), Study the change of the phase space of the standard map as changes from 0 to 2 . S
MEE 201 Advanced Dynamics. 11/8/2007.
Homework set No. 4 Due Thursday, 11/15/2007 in morning class. 1. Consider a mathematical pendulum of length l and mass m, moving in the eld of gravity. The pendulum is moving in a viscous liquid which exerts a force o
MEE 201 Advanced Dynamics. 10/30/2007.
Homework set No. 3 Due Tuesday, 11/6/2007 in class. 1. Consider the following linear dynamical system on R2 : x = ax + by, y = cx + dy. (1) (2)
In matrix form, this system can be written as x = Ax for a matrix A, wh
MEE 201 Advanced Dynamics. 10/23/2007.
Homework set No. 2 Due Tuesday, 10/30/2007 in class. 1. Consider the system of two oscillating equal masses given by mx1 mx2 = = kx1 + c1 (x1 x2 ) + c2 (x1 x2 )3 , kx2 c1 (x1 x2 ) c2 (x1 x2 ) .
3
(1) (2)
a Is this a
MEE 201 Advanced Dynamics, Fall 2007: Final Exam
12/7/2007
Exam is take home, open notes, books and homeworks, no internet please. It is due Friday, 12/14/2007 to Melecia Valdez in the front oce of Mechanical and Environmental Engineering Department, befo
ME201 Advanced Dynamics (Fall 2007) Bonus-1 Solutions (100 pts) 1. (30 pts)Consider the following equation of motion for a mass-spring system; mx = kx x3 where m is the mass, k is the spring constant and is a positive constant representing the strength of
MEE 201 Advanced Dynamics. 10/16/2007.
Bonus set No. 1 For extra credit, present 10/23/2007 in class. 1. Consider the following equation of motion for a mass-spring system: mx = kx x3 . where m is the mass, k is the spring constant and is a positive const
ME201 Advanced Dynamics (Fall 2007) Midterm Solution (100 pts) Consider the system shown in the gure. Planar pendulum (no gravity) of mass m is free to rotate around the point O by 360 : The mass is connected to point O by a massless inextensible bar of l
MEE 201 Advanced Dynamics. 10/16/2007.
Homework set No. 1 Due Tuesday, 10/23/2007 in class. 1. Write Newtons equations of motion for two particles of masses m1 and m2 interacting via Newtons law of gravitation. How many degrees of freedom does the system
ME201 Advanced Dynamics (Fall 2007) HW-4 Solution (100 pts) 1. 50pts Consider a mathematical pendulum of length l and mass m, moving in the eld of gravity. The pendulum is moving in a viscous liquid which exerts a force of magnitude c in the direction opp