nodicity - NODICITY One of the important ways that physical...

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NODICITY One of the important ways that physical system behavior differs between domains is the way elements may be connected. Electric circuit elements may be connected in series or in parallel — networks of arbitrary structure may be assembled This not true of all domains Electric circuit elements have a special property called nodicity Mod. Sim. Dyn. Sys. Nodicity page 1

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N ODICITY Nodicity means that a network element (or sub- network) has behavior analogous to a “node” in an electric circuit. Consider a “delta” network of resistors Assuming linear inductors, the relation between currents and voltages may be written as i 1 i 2 i 3 = G 1 +G 2 –G 2 –G 1 –G 2 G 2 +G 3 –G 3 –G 1 –G 3 G 1 +G 3 e 1 e 2 e 3 where G i is conductance i i = G i e i 1 G i = R i Note that this conductance matrix is singular — the sum down each column is zero. i.e., the sum of currents flowing into the network is zero i 1 + i 2 + i 3 = 0 Mod. Sim. Dyn. Sys. Nodicity page 2
As a result, the three constitutive equations describing the currents may be re-arranged as follows i 1 i 2 = G 1 +G 2 –G 2 –G 2 G 2

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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.141 taught by Professor Nevillehogan during the Fall '06 term at MIT.

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nodicity - NODICITY One of the important ways that physical...

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