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The first aim of the work is to derive the chosen robot model dynamics using Lagrangian methods and develop a Matlab/Simulink tool for the simulation of the model.
A variety of other conservation laws can be deduced from symmetry or invariance properties of the corresponding Lagrangian or Hamiltonian of the system.
One type of hydrodynamical code (called a Lagrangian code) models the 2 gas as lots of particles and the most obvious way to calculate the gas density in this case is to simply place a sampling volume around each particle and calculate the density by multiplying the number of particles in the volume by the mass of each particle and then dividing by the volume.
The use of the dual-variable Lagrangian yields the following optimization problem:
Symmetry breaking is termed spontaneous when there is no explicit term in a Lagrangian which manifestly breaks the symmetry.