The shock absorber from LABEIN

Communicated by S. Casado (LABEIN)

The system under consideration has 27 equations and 27 unknowns with several parameters whose value is only known approximately. Two kind of unknowns are considered:

• the pressures: $\{P_i:1\leq i\leq 14\}$.
• the flows: $\{q_j: 1\leq j\leq 15\}$.

The total degree of the equations is equal to one or two. These come from two different physical conditions: flow equilibrium in the different components of the electric-hydraulic circuit and pressure value in every node of such a diagram. The flow equilibrium equations are:

$$\matrix{ \hfill q_1&=&q_2\hfill \cr \hfill q_2&=&q_3+q_7\hfi... ...q_6+q_{10}&=&q_{11}\hfill \cr \hfill q_{11}&=&q_{12}\hfill \cr}$$

and the pressure equations are:

$$\matrix{ \hfill P_2-P_1&=&q_1^2\displaystyle{{\rho}\over{2}}... ..._8^3}}+k_{\eirm gr}\displaystyle{1\over{S_8^2}}\bigg]\hfill\cr}$$

$$\matrix{\hfill P_{10}-P_9&=&q_{10}^2\displaystyle{{\rho}\ove... ...laystyle{{(S_{14}-S_{13})^2}\over{S_{14}^2S_{13}^2}}\hfill\cr }$$

The initial data is given by the knowledge of the pressure and flow at the entry node:

$$q_1=Q,\quad P_1=0$$

In this case, only real solutions are required.