[Solved]Task 1 Solving Non Linear System Equations Two Unknowns Y F X B X0yo Shown Sketch Wheel Ra Q37156393
Need to solve using MATLAB
Non linear system of equations
Task 1: Solving a non-linear system of equations with two unknowns y-f(x) B (x0.Yo) As shown in the sketch, a wheel with radius R should roll along a path which is defined by function beschrieben wird. Es sei M (x1,y1) der Mittelpunkt des Rades und B (x0,y0) der Berührpunkt des Rades mit der Bahnkurve. Let M-(x1,y1) be the center of the wheel and B- (x0,y0) the point of contact of the wheel with the trajectory curve. Note that the center M is not exactly above the point of contact B. Therefore, you can specify x1 for an animation of the motion sequence, but in general it is then y1 f(x1). In order to be able to characterize the wheel you have to calculate yi as follows: The normalized normal vector directed upwards to the trajectory at the point of contact B-(x0, y0) is From the point of contact B, one arrives in the direction of the normal vector n at a distance R from the center M If you use (2) and (3), you get -F(xo 4 In the form of zeros, the three equations (1) and (4) form a nonlinear system of equations for the calculation of the three unknown quantities x0,y0 and y1, where, as already mentioned, x1 is given. The length L of the distance travelled by the wheel while rolling on the curve from x-a tox-b is calculated by an integral turn by angle while mo Your tasks: a) Think of an interesting wavy yex). No simple sine or cosine b) Write a Matlab program that solves the nonlinear equation system for a suitable range of x values and animates the wheel to roll on the trajectory. The wheel should be drawn so that the rolling can be seen and controlled. Calculate f”(x ) with a second order difference formula Show transcribed image text Task 1: Solving a non-linear system of equations with two unknowns y-f(x) B (x0.Yo) As shown in the sketch, a wheel with radius R should roll along a path which is defined by function beschrieben wird. Es sei M (x1,y1) der Mittelpunkt des Rades und B (x0,y0) der Berührpunkt des Rades mit der Bahnkurve. Let M-(x1,y1) be the center of the wheel and B- (x0,y0) the point of contact of the wheel with the trajectory curve. Note that the center M is not exactly above the point of contact B. Therefore, you can specify x1 for an animation of the motion sequence, but in general it is then y1 f(x1). In order to be able to characterize the wheel you have to calculate yi as follows: The normalized normal vector directed upwards to the trajectory at the point of contact B-(x0, y0) is From the point of contact B, one arrives in the direction of the normal vector n at a distance R from the center M If you use (2) and (3), you get -F(xo 4 In the form of zeros, the three equations (1) and (4) form a nonlinear system of equations for the calculation of the three unknown quantities x0,y0 and y1, where, as already mentioned, x1 is given. The length L of the distance travelled by the wheel while rolling on the curve from x-a tox-b is calculated by an integral
turn by angle while mo Your tasks: a) Think of an interesting wavy yex). No simple sine or cosine b) Write a Matlab program that solves the nonlinear equation system for a suitable range of x values and animates the wheel to roll on the trajectory. The wheel should be drawn so that the rolling can be seen and controlled. Calculate f”(x ) with a second order difference formula
Expert Answer
Answer to Task 1: Solving a non-linear system of equations with two unknowns y-f(x) B (x0.Yo) As shown in the sketch, a wheel with… . . .
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