Three dimensional rotating coordinate frame (to be written) Kinematic constraints A kinematic constraint is any condition relating properties of a dynamic system that must hold true at all times. Below are some common examples: Rolling without slipping An object that rolls against a surface without slipping obeys the condition that the velocity of its center of mass is equal to the cross product of its angular velocity with a vector from the point of contact to the center of mass, oldsymbol_G(t) = oldsymbol imes oldsymbol_. For the case of an object that does not tip or turn, this reduces to v = R ω. Inextensible cord This is the case where bodies are connected by some cord that remains in tension and cannot change length. The constraint is that the sum of all components of the cord, however they are defined, is the total length, and the time derivative of this sum is zero. References and notes
Posted on: Mon, 16 Sep 2013 16:46:32 +0000
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