CHAPTER 7 STRINGERS AND SHEAR PANELS
For semi-monocoque structures with stringers and shear panels, one can use a simplified model to determine the following: Axial stress on stringers Shear flows in the shear panels
7.1 Simplified Model with Stringers an

CHAPTER 4 TORSION OF THIN-WALLED STRUCTURES
Closed sections under torque Single-cell closed sections Thin-walled open sections Multi-cell closed sections
Consider a slender body such as a wing or a fuselage subjected to torsional moment or torque.
( x) :

Orbital maneuvers Changing orbits in-plane: a, e, , plane change: i, In planning a maneuver, usually the two most important quantities are total v (fuel consumption), total time of transfer (to complete the maneuvers), though other considerations may come

Attitude parameters There are several dierent parameter sets to describe attitude, among them Euler angles (313, 321, etc.) direction cosines, Euler parameters/quaternions. Much as there are 6 quantities to minimally specify the orbital state of a satelli

v at each maneuver Triangle, v1, delta v1, vt with angle alpha1 Speeds for circular orbits are determined by radii, 2 = , 2= , vi vf ri rf and the Hohmann analysis gives the transferorbit speeds,
2 vta =
2 2 ri ri + rf 2 2 2 vtb = rf ri + rf
For the two m

Solve for intersection of rotated ellipses An equation of the form a cos + b sin = c can be solved by c cos a where tan = b/a. (Variables a, b, c are just coecients, not semimajor axis etc.) The two signs correspond to the two intersection points of the e

Phasing worked example Vallado Example 68, pp. 348349 Given: ai = atg = 2 ER = 12756 km, = 20 so the interceptor leads the target. Find phasing time and v . The angular velocity is ntg = 4.382 104 rad/s Because the interceptor is not that far from the tar

Bi-elliptic details Use the Hohmann transfer computation, but apply it twice. Call rB the geocentric distance of the intermediate orbit. The semimajor axes of the two transfer ellipses: rB + rC rA + rB , at2 = . at1 = 2 2 On the two transfer ellipses, we

Recalculate example with f and g functions Once again, suppose we have a satellite which has Cartesian IJK
r0 =
r0 =
26981. 28850. km 13174. 1.2784 0.83017 km/s 0.57114
What is its state 24 hours later?
L. Healy ENAE404 Spring 2007 Lecture 12 (Mar. 6)
1

Computation of orbital elements from Cartesian
Ref.: Curtis Sec. 4.4, Vallado Section 2.5 We know about orbital elements, but how do we nd them? If were given Cartesian state vector (position vector r and velocity vector r ), we can compute them using the