This section allows the simulation of different systems with different sets of initial conditions, The systems are characterized by different State Matrices, \underline{\underline{A}} . For this section to be more useful, three State Matrices are presented for you to fill the values of the elements. To each one, three sets of initial conditions are presented for you to fill the values too. This will allow you to examine the trajectories of the state vector of each system for each set of initial conditions. Since systems can have State Matrices with different eigenvalues, their behaviors may be compared.

Three sets of boxes are presented below. In each one, you must type: (1) the four elements of the State Matrix; and (2) the two elements of the vector of initial conditions for each one of the three initial conditions. Then, click Send and observe the graphics showing the trajectories of the state vectors as functions of time.

If you use the three sets, you will be able to compare three different behaviors yielded by the State Matrices.

Attention: Start with Case 1, then go to Case 2 and finally to Case 3. If you decide to go back to Case 1, all options will be cleared.

As a suggestion repeat the simulations for State Matrices with different sets of eingenvalues since the trajectories will vary.

Case 1:

\underline{\underline{A}} =			\underline{x}^{1}(0) =		\underline{x}^{2}(0) =		\underline{x}^{3}(0) =

Case 2:

\underline{\underline{A}} =			\underline{x}^{1}(0) =		\underline{x}^{2}(0) =		\underline{x}^{3}(0) =

Case 3:

\underline{\underline{A}} =			\underline{x}^{1}(0) =		\underline{x}^{2}(0) =		\underline{x}^{3}(0) =