crib - SYSC 3600 Crib Sheet &Inertial¡ Components...

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Unformatted text preview: SYSC 3600 Crib Sheet &Inertial¡ Components (these components store energy) Component Energy Key Equation Notes moving mass 2 2 1 mv v m F m F v & & = = / m = mass F = applied force rotating mass 2 2 1 ω J ω τ τ ω & & J J = = / J = moment of inertia τ = applied torque inductor 2 2 1 Li i L e L e i & & = = / i = current e = voltage &Capacitive¡ Components (these components store energy) Component Energy Key Equation Notes linear spring 2 2 1 kx kx F k F x = = / x = spring displacement F = force k = spring constant (N/m) torsion spring 2 2 1 θ k θ τ τ θ k k = = / θ = spring displacement τ = torque k = spring constant (N-m/radian) capacitor 2 2 1 Ce Ce q C q e = = / e = voltage q = charge C = capacitance &Dissipative¡ Components (these components dissipate energy) Component Key Equation Notes damper cv F c F v = = / c = damping coefficient F = force viscous friction kv F k F v = = / k = friction coefficient F = force rotational damper ω τ τ ω c c = = / c = damping coefficient τ = torque rotational viscous friction ω τ τ ω k k = = / k = friction coefficient τ = torque resistor iR e R e i = = / i = current e = voltage Gearbox: Motor/Generator 2 2 2 1 1 1 1 2 1 2 1 1 2 2 ) / ( ) / ( power power n n n n = = = = = ω τ ω τ ω ω τ τ MECH b ELEC t b t b t t power ie power k e k e k i i k = = = = = = = τω ω ω τ τ / / Matrix (1 input, 1 output): [ ] [ ] [ ] [ ] u x y u x x y u x 11 1 1 1 11 2 1 variables state D C C B B A A A output input s s s N N NN N N + = + = = = = = L L L L L L L L & L A is the n by n state matrix B is the n by 1 input matrix C is the 1 by n output matrix D is the 1 by 1 d rect transmission matrix Units: s s s s s m kg m N s coulomb m kg amp volt ohms R m kg s coulomb volt coulomb farad C coulomb m kg s amp volt henry L s coulomb m kg coulomb m N V s coulomb amp I s coulomb m kg amp m N k s m kg s m N b s m kg m N k s kg s m N b s kg m N k m kg J t s s = = = = = Τ = = = = = = = = = = = = = = = = = = = = = = = = )...
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This note was uploaded on 07/16/2009 for the course SYSC 3600 taught by Professor John bryant during the Winter '08 term at Carleton CA.

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crib - SYSC 3600 Crib Sheet &Inertial¡ Components...

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