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Design of a Linear Quadratic Regulator balance controller for the Inverted Pendulum. After manually initializing the pendulum in the upright vertical position, the balance controller moves the rotary arm to keep the pendulum in this upright position. Moreover it is capable of balancing itself, even if minor external disturbances are given.
Shown here is a screenshot of two orthogonal slope fields y' = sin(x) + sin(y), y' = -1/(sin(x)+sin(y)), and their respective solutions sets in red. As highlighted by orange circles, the solution of the differential equation y' = -1/(sin(x)+sin(y)) displays continuity where th
A simple Python program, which allows the automatic symbolic creation of the Lagrange equations for pendulums and similar objects. Furthermore a numerical solver is used in order to approximate the solutions.
Shown here is a screenshot of two orthogonal slope fields y' = sin(x) + sin(y), y' = -1/(sin(x)+sin(y)), and their respective solutions sets in red. As highlighted by orange circles, the solution of the differential equation y' = -1/(sin(x)+sin(y)) displays continuity where th