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Regarding whether the cart moves horizontally or not, you have to look at the horizontal forces acting ON the cart. If the cow pulls on the cart, that is one horizontal force acting ON the cart. There is probably friction acting on the cart in the opposite direction. That's why most cow/cart systems move at constant speed. But the cart pulling on the cow is not a force on the cart.

I can answer questions from Newtonian, Lagrangian, and Hamiltonian mechanics. In particular, I can help with derivations and applications of formulas and theorems. Some example topics include stability analysis, deriving equations of motion, Noether's theorem, cart on a pendulum, double pendulum, etc... In general, I won't solve homework problems, but I can give advice on how to approach problems.

I use classical mechanics often for my research in dynamical systems and control theory. In particular, I have experience working with the three body problem and numerical integration of mechanical systems, such as the double pendulum, using Runge-Kutta and variational integrators.**Organizations**

SIAM
AIP
APS
AIAA
IEEE**Publications**

AIAA Aerospace Sciences Meeting and Exhibit [2008, 2009].
IEEE Photovoltaic Specialist [2009].
For these publications, see http://carlsbad.princeton.edu/~steve/papers/**Education/Credentials**

I earned my B.S. in Mathematics from Caltech in 2006. I am currently a PhD. Candidate in Mechanical and Aerospace Engineering at Princeton. I expect to graduate in 2011.**Awards and Honors**

Athena-Feron Scholarship Award for Excellence in Mathematical Coursework [2007],
Princeton MAE Second Year Fellowship for Research Excellence [2007],
Gordon Wu Fellowship [2006-2010],
Caltech Summer Undergraduate Research Fellowship [2003-2005].