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CEE 212—Dynamics

© Keith D. Hjelmstad

CP 2—Contact Benchmark case

The benchmark case will be used to demonstrate that your code works for the in-class code check (consult course schedule to see when that is).

CP 2 - Contact (Curved Surface)

PHYSICAL PROPERTIES Acceleration of gravity 9.810 Mass 2.000 Drag coefficient 0.000 Coefficient of restitution 0.950 Initial time (to) 0.000 Final time (tf) 23.500 Lowest elevation allowed -2.000

Constraint function: g(x,y) = y - (a*x^2 + b*x + c) Parameters (a, b, c) 0.050 0.000 2.000

INTEGRATION OF EQUATIONS Time increment (dt) 0.010 Numerical integration (beta) 0.500 Tolerance for Newton 1.0e-08 Max iterations for Newton 10 Number of time steps 2350 Number of steps to report 2000 Output every 2 steps

INITIAL CONDITIONS Initial position (x) 5.000 Initial position (y) 15.000 Initial velocity (x) 5.000 Initial velocity (y) 10.000

Contact History time frac its Eloss

2.1193 0.9297 3 9.81487e+00 3.6571 0.7825 3 2.91869e+01 6.4447 0.7569 3 8.29254e+00 8.0051 0.0385 3 2.45728e+01 9.9514 0.6323 3 6.48616e+00 12.1315 0.0092 3 1.85508e+01 13.1119 0.0431 3 8.90182e+00 15.7580 0.6036 3 7.78109e+00 16.7259 0.7970 4 1.44677e+01 18.0576 0.1682 3 4.82144e+00 20.2249 0.7313 3 6.88974e+00 21.0254 0.0438 3 1.06132e+01 22.0816 0.6222 3 4.12139e+00

The following table gives the times, the fraction , the number of iterations to get the fraction to within the tolerance, and the energy loss in contact for each hit.

CEE 212—Dynamics

© Keith D. Hjelmstad

CP 2—Contact Benchmark case

0 5 10 15 20 25 0

50

100

150

200

250

300

350

400

450

t

U (b

lu e)

, T

(r ed

) E

(b la

ck )

Energy vs. Time

-15 -10 -5 0 5 10 15

5

10

15

20

x

y

2D Trajectory