Monday, December 18, 2006

Long time..no see :-)

Ok...so this is a post after 9 months...
Well, a lot has happened in the interim period ...my research focus has taken new and unxpected directions...
This past semester, I was trying to learn the some graduate level dynamical systems theory...with focus on chaos. Topics I covered (in varying detail) were:
Some perturbation/averaging stuff
Local Bifurcations
Symbolic dynamics and chaos...Smale horseshoe!!
Hamiltonian systems...lots of it. integrability..nearly integrable systems...intro to KAM
Melnikov theory (in N-dimensions also :-( )
Some Chaotic transport stuff
Read some papers about low fuel trajectories in space missions
Right now reading about twist maps and generally, transport in Hamiltonian systems
Also, thinking about a writing a proposal to apply transport theory for calculation of impact ejecta...

Friday, March 17, 2006

Grazing Bifurcations...

Ok, So now getting on to what I am upto this semester. I am basically learning new things in Dynamical systems theory everyday. The problem I am working on (actually just reading the papers as of now:-)) is regarding grazing bifurcations. Lets say you have a spring mass damper..system, periodically forced. Now if we place an obstacle in the path, which has grazing intersection (velocity during impact=0)with the body =>its called a grazing trajectory. Now if we slightly change the parameter (hence changing the position of the obstacle) and have low velocity impacts..there is a lot of interesting phenomenon that can take place. The objective is to come up with rigrous conditions which define the persisitence of periodic orbits when we change the parameters...the resulting bifurcations are called grazing bifurcations. A lot of work has been done by a fellow student (who is on the verge of finishing his PhD. on the topic ) and hence I have a lot of reading to do.

Wednesday, February 22, 2006

Watever...

So, this being my first 'non-introductory' post, let me explain what I am learning these days and what I hope to do in the future.
I graduated with a Mechanical Engg. degree from India, in May-05. During my 4 years at college, I took almost all the dynamics and controls courses I could, ranging from the mandatory kinematics/dynamics of machinery to mechanical vibrations, modern control (didnt do well on that one :-(( ), and nonlinear vibrations. In my first semester last fall here at Virginia Tech, I took a grad level intermediate dynamics course by a very fine professor. The stuff covered ranged from 3-d dynamics using euler angles, and for the most part, lagrangian approach to dynamics, with fair amount of lagrange multipliers thrown in. The course was rigorous and we solved a lot of practical problems too. I also took a first course in real-analysis, again taught very well by a prof from Maths dept. It was my first rigorous course in analysis and though I was VERY uncomfortable in the beginning, I was able to adapt and finally did quite well on the course. This course was recommended by a senior grad student who has since graduated with a PhD. in nonlinear control theory.
So this semester, I am taking the next course in dynamics (Advanced dynamics) and the second course in Reals, again taught by the same professors mentioned above. The dynamics course has been pretty boring so far, lots of algebra .and the reals course isn't proving to be too tough.

Tuesday, February 21, 2006

Hi....

So I have started writing a supposedly technical blog...which i know not many are going to read, but then same is the case with research papers :-) .....i am basically gonna talk about what i am into these days...dynamics...dynamical systems...nonlinear dynamics...multibody mechanics...etc etc. I also hope to find some time to write about game-programming, which was my first love in college..though I havent done any for the past year and a half. I don't have a higher purpose in writing this blog...needed someplace to write it all down...just for the record. Also, I noticed that most of tech blogs invariably talk about computers/IT/electronics...and couldn't find many blogs that talked about stuff i am into...so let's get started.