New PDF release: Dynamic system modeling and control

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Normally these forces are small, except at high velocities. 20 Viscous damping between two bodies with relative motion A damping force is proportional to the first derivative of position (velocity). Aerodynamic drag is proportional to the velocity squared. 21 in vector and scalar forms. The drag force increases as the square of velocity. Normally, the magnitude of the drag force coefficient ’D’ is approximated theoretically and/or measured experimentally. The drag coefficient is a function of material type, surface properties, object size and object geometry.

Where the mechanism has been broken the contact forces must be added to both of the separated pieces. 28. At joint A the forces are written as two components in the x and y directions. For joint B the force components with equal magnitudes but opposite directions are added to both FBDs. 28 Note: Don’t forget that forces on connected FBDs should have equal magnitudes, but opposite directions. 3 SYSTEM EXAMPLES An orderly approach to system analysis can simplify the process of analyzing large systems.

F result Block begins to slip and the applied force exceeds the resultant and acceleration begins. Fs Fk Fapplied Fs Fg N F Fk = µk N F k, F s Fs ≤ µs N Note: When solving problems with friction remember that the friction force will always equal the applied force (not the maximum force) until slip occurs. After that the friction is approximately constant. In addition, the friction forces direction opposes applied forces, and motion. 24 Many systems use kinetic friction to dissipate energy from a system as heat, sound and vibration.

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Dynamic system modeling and control by Jack H.

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