Any tips of Matlab or Mathematica usage as well as general code should go here.

We can also put general information on optimization algorithms such as SVD / SVM / Genetic Algorithms / Neural Nets / LWR here.

Libraries

• Stony Brook Algorithm Repository: collection of algorithms and libraries
• BLAS: Basic Linear Algebra Subroutines
• LAPACK: Linear Algebra Package
• SPRNG: Scalable Parallel Random Number Generator (ubuntu package: libsprng2)
• FANN: Fast Artificial Neural Nets

Deriving Dynamics of the Two-Wheel Manipulator (Using Lagrangian Approach)

I tried to derive the dynamics of the two-wheel manipulator using Lagrangian approach and transform it to the state space representation. Since the derivation is really messy, using Mathematica is a good way to get the dynamics systematically and symbolically. Here I found some useful tips about Mathematica that I want to share
• Be careful when using a subscript in the variable. Sometimes Mathematica will think that the subscript itself is not actually a subscript but a function variable. For example, let where is a variable and is a constant. Suppose we take the derivative of with respect to , we should get . However, actually D[x,t] which is not what we expected. The problem can be solved by changing the subscript to something else or just not using a subscript.
• When we need to calculate the norm of a vector . Let's say . Using Norm[], sometimes may not be good since
  Norm[v]. The absolute value will give us a problem when we want to simplify the expression. Instead, find another way to define a norm e.g. use a dot product Sqrt[v.v] . This will allow us to avoid the absolute sign.