SimReal: DiffInt - Vector - Application - Piston
Position and velocity vectors (the derivative of position vectors) This application shows an example of the use of position vectors and the corresponding velocity vectors (the derivative of position vectors). The piston rod is moving as a SHM: x(t) = Asin(ωt) where A is the amplitude and ω is the angular velocity. The key point in this application is to better understand (through a practical example) the differentiation of vectors. We have three position vectors: r_{CA}, r_{CB} and r_{BA}. We have the following relation (mark the checkboxes 'Position' and 'Txt' to see this relation): r_{CA} = r_{CB} + r_{BA} Differentiation of this position equation gives us the corresponding velocity vectors: v_{A} = v_{B} + v_{BA} The velocity vector v_{BA} is the velocity of A relative to B (mark the checkbox 'Velocity Rel'): Notice that the vector v_{B} is normal to the arm CB (the arm CB has constant length and B is therefore moving in a circle around C) and the vector v_{AB} is normal to the arm BA (the arm BA has constant length and A is therefore moving in a circle around B ). Explanation of the control objects: - Piston : Hide the piston - Position vector : Draw position vectors CA, CB and BA - Velocity vector : Draw velocity vectors of A and B - Velocity A/B : Draw velocity of A relative to B - Txt : Show text on the piston system - Formula : Show important formula of the piston movement - Angular Velocity : Change the angular velocity of the piston rodClick the pushbutton 'Run' to start the simulation. Use the scrollbar 'Angular Velocity' to change the angular velocity ω. |