Chapter Three – Practice Exercises
3a)
Using the data from the Saturn launch example in chapter three calculate the family of quadratic splines for the following different Selected Interval Data Points (knots) and compare to the example.
Saturn 5 Rocket Launch Data
| x (time in minutes) | y (velocity in 1000 ft per second |
|---|---|
| 0 | 1 |
| 1 | 2 |
| 2.5 | 9 |
| 3 | 9.2 |
| 4 | 10 |
| 5 | 12 |
| 6 | 14.5 |
| 7 | 17 |
| 8 | 20 |
| 8.75 | 23 |
| 9 | 23.5 |
| 10 | 24 |
| 11 | 25.5 |
| 11.25 | 25.9 |
| 11.5 | 25.9 |
Selected Interval Points (knots)
| x | y | Interval |
|---|---|---|
| 1 | 2 | start of first interval |
| 2.5 | 9 | 1st stage separation |
| 8.75 | 23 | 2nd stage separation |
| 11.25 | 25.9 | 3rd stage shutdown |
3b)
Using the table in 3a) for time = 7.5, conduct a Direct Method Cubic Interpolation. Show the resulting polynomial in standard form and graph the solution manually or with your favorite graphing tool.
(Solution given)
Feedback/Errata