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Download Models Dynamic Systems. Dynamic Systems Modeling and Control by H Jack PDF

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Extra info for Models Dynamic Systems. Dynamic Systems Modeling and Control

Sample text

2. Define positions and directions for any moving masses. 25 selection of reference points. 3. Draw free body diagrams for each component, and add forces (inertia is optional). 4. Write equations for each component by summing forces. (next chapter) Combine the equations by eliminating unwanted variables. (next chapter) Develop a final equation that relates input (forcing functions) to outputs (results). Note: When deriving differential equations, the final value can be checked for errors using unit analysis.

2. Define positions and directions for any moving masses. 25 selection of reference points. 3. Draw free body diagrams for each component, and add forces (inertia is optional). 4. Write equations for each component by summing forces. (next chapter) Combine the equations by eliminating unwanted variables. (next chapter) Develop a final equation that relates input (forcing functions) to outputs (results). Note: When deriving differential equations, the final value can be checked for errors using unit analysis.

After this, the equation is rearranged into Hooke’s law, and the equivalent spring coefficient is found. 32 First, draw FBDs for P and M and sum the forces assuming the system is static. K S1 y 2 P + ∑ Fy = K S1 y 2 – K S2 ( y 1 – y 2 ) = 0 (1) K S2 ( y 1 – y 2 ) K S1 K S2 ( y 1 – y 2 ) K S2 M + ∑ Fy P = K S2 ( y 1 – y 2 ) – F g = 0 (2) Fg M y1 Next, rearrange the equations to eliminate y2 and simplify. (1) becomes K S2 ( y 1 – y 2 ) – F g = 0 Fg y 1 – y 2 = --------K S2 Fg y 2 = y 1 – ---------K S2 (2) becomes (3) K S1 y 2 – K S2 ( y 1 – y 2 ) = 0 (4) y 2 ( K S1 + K S2 ) = y 1 K S2 Fg   sub (3) into (4)  y – --------- ( K + K ) = y K S2 1 S2  1 K S2 S1 Fg K S2 y 1 – ---------- = y 1 --------------------------K S2 K S1 + K S2 K S2   Fg = y 1  1 – ---------------------------- K S2 K S1 + K S2   K S1 + K S2 – K S2 Fg = y 1  -------------------------------------------K  K S1 + K S2  S2  K S1 K S2  F g = y 1  ---------------------------  K S1 + K S2 Finally, consider the basic spring equation to find the equivalent spring coefficient.

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