MAE 340 Lecture Notes - Lecture 7: Asteroid Family, Northrop Yb-35, Settling Time

• School: University at Buffalo
• Department: Mechanical & Aerospace Engr
• Course: MAE 340
• Professor: J.Mook

Document Summary

Consider again the general form of a single nth-order lti ode: General form of the particular solution an dnx(t) dtn + an 1 dn 1x(t) dtn 1 + + a1 dx(t) dt. We have previously seen that the complete solution may be written as the sum of a homogeneous solution and a particular solution, and that the homogeneous solution may be written in the general form xh(t) = ae t. The general form of the particular solution may be written xp(t) = c1f (t) + c2 f (t) + c3 f (t) + + cn+1 dnf (t) dtn (2) where c1, c2, . , cn+1 are constants which are determined by substituting eq. (2) into eq. (1). = c1t2 + (2c1 + 2c2)t + ( 7c1 + 2c2 + 2c3) (3) (4) Although we could solve for xp using eq. (4), there"s no need to do so. We simply solve for xp using the form of eq. (5).