Electromechanical Dynamics (Part 1).0058

Electromechanical Dynamics (Part 1).0058 - 2.2.2a motion is...

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Mechanics X2 - X1 = X(t) Fig. 2.2.1 A position source: (a) physical; (b) schematic. position source z(t) constrains the relative positions of the two nodes to X 2 - X 1 = X(t); (2.2.1) the sign is determined by the + and - signs associated with the source. In Fig. 2.2.1b we give the circuit representation of the position source. The circuit is a pictorial representation of the scalar equation (2.2.1) and as such is completely analogous to the representations in circuit theory. Because (2.2.1) is valid regardless of other mechanical elements attached to the nodes, the ideal position source can supply an arbitrary amount of force. In a similar way we can define a velocity source v(t) that constrains the relative velocity of the two nodes to dx 2 dl = v(t). (2.2.2) dt dt The circuit is as shown in Fig. 2.2.1b with x replaced by v. A different kind of ideal mechanical source is a force source for which nomenclature is given in Fig. 2.2.2. In the physical representation of Fig.
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Unformatted text preview: 2.2.2a motion is constrained to the vertical and the forcef(t) is vertical. The position of the arrow indicates the direction of positive force, and the convention we use here is that, with the arrow as shown and a positivef(t), the force tends to push the two mechanical nodes apart exactly as if one were standing on node ax and pushing upward on node X, with the hands. The circuit representation of this force source is given in Fig. 2.2.2b. In the circuit our convention is that with the arrow as shown [f(t) positive] the force tends to increase z 2 and decrease x 1 . The sources of Figs. 2.2.1 and 2.2.2 have been specified for translational systems. We can also specify analogous sources and circuits for rotational 2.2.1 l A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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