A new analytical tool is proposed to aid in the design and performance evaluation of advanced guided projectile concepts. A projectile linear theory applicable to aerodynamically asymmetric configurations is created, leading to a linear, periodic dynamic system. Utilizing concepts in Floquet theory, stability of asymmetric projectile configurations is explored. While stability of many asymmetric projectile configurations can be accurately predicted using averaged linear, constant coefficient system dynamics, there are some configurations where the use of linear periodic systems theory is required for accurate stability prediction. This fact is shown by comparing stability boundaries of an example projectile configuration using the conventional projectile linear theory model and the new periodic projectile linear theory model.
MorrisonPH. A lesson learned about cannon launched guided projectiles. J Guidance Navigat Control1980; 3: 154–157.
2.
MorrisonPHBerntsonDS. Guidance and control of a cannon-launched guided projectile. J Spacecraft Rockets1977; 14: 328–334.
3.
GrubbNDBelcherMW. Excalibur: new precision engagement asset in the warfight. Fires2008(Oct–Dec): 14–15.
4.
FresconiF. Guidance and control of a projectile with reduced sensor and actuator requirements. J Guidance Control Dynam2011; 34: 1757–1766.
5.
FresconiFHarkinsT. Experimental flight characterization of asymmetric and maneuvering projectiles from elevated gun firings. J Spacecraft Rockets2012; 49: 1120–1130.
6.
CooperGCostelloMFresconiF. Flight stability of asymmetric projectiles with control mechanisms. J Spacecraft Rockets2011; 49: 130–135.
7.
Fresconi F, Celmins I and Fairfax L. Optimal parameters for maneuverability of affordable precision munitions. In: 2012 AIAA aerospace sciences meeting proceedings, Orlando, FL, January 12 2012.
8.
FresconiFCooperGRCelminsI. Flight mechanics of a novel guided spin-stabilized projectile concept. J Aerospace Eng2011; 226(3): 327–340.
9.
FowlerRGallopELockC. The aerodynamics of the spinning shell, London: Philosophical Transactions of the Royal Society of London. Series A, 1921, pp. 295–387.
10.
McCoyRL. Modern exterior ballistics, Atgen, PA: Schiffer Military History, 1999.
11.
EtkinB. Dynamics of atmospheric flight, Dover, DE: Courier Dover Publications, 2012.
12.
SzidarovskyFBahillAT. Linear systems theory, 2nd ed. Boca Raton, FL, USA: CRC Press, 1998.
13.
RogersJCostelloM. Design of a roll-stabilized mortar projectile with reciprocating canards. J Guidance Control Dynam2010; 33: 1026–1034.
14.
Murphy CH. Symmetric missile dynamic instabilities: A survey. In: 18th AIAA aerospace sciences meeting. Pasadena, CA, USA, 14–16 January 1980, paper no. AIAA1980-0320. USA: AIAA.
15.
HodappAE. Effect of mass asymmetry on ballistic match of projectiles. J Spacecraft Rockets1976; 13: 757–760.
16.
WeberDJ. Simplified method for evaluating the flight stability of liquid-filled projectiles. J Spacecraft Rockets1994; 31: 130–134.
17.
MurphyCH. Angular motion of a spinning projectile with a viscous liquid payload. J Guidance Control Dynam1983; 6: 280–286.
18.
Cobb KK and Whyte RH. Effects of moving components on the motion of a 20-mm projectile. In: 11th AIAA aerodynamics testing conference. New York: AIAA, 1983, pp. 94–103.
19.
HodappAE. Passive means for stabilizing projectiles with partially restrained internal members. J Guidance Control Dynam1989; 12: 135–139.
20.
SoperWG. Projectile instability produced by internal friction. AIAA J1978; 16: 8–11.
21.
CostelloMPetersonA. Linear theory of a dual-spin projectile in atmospheric flight. J Guidance Control Dynam2000; 23: 789–797.
22.
MurphyCH. Instability of controlled projectiles in ascending or descending flight. J Guidance Control1981; 4: 66–69.
23.
CooperG. Influence of yaw canards on the yaw growth of spin stabilized projectiles. J Aircraft2001; 38: 266–270.
24.
Guidos B and Cooper G. Closed form solution of finned projectile motion subjected to simple in-flight lateral impulse. AIAA Paper 2000 0767. New York: AIAA, 2000.
25.
BurchettBPetersonA. Prediction of swerving motion of a dual-spin projectile with lateral pulse jets in atmospheric flight. Math Comput Model2002; 35: 821–834.
26.
OllerenshawDCostelloM. Model predictive control of a direct fire projectile equipped with canards. J Dynam Syst Measurement Control2008; 35: 114–114.
27.
Cooper G and Fresconi F. Flight stability of an asymmetric projectile with activating canards. In: AIAA atmospheric flight mechanics conference, Toronto, CA, May 2010.
28.
MontalvoCCostelloM. Effect of canard stall on projectile roll and pitch damping. J Aerospace Eng2011; 225: 1003–1011.
29.
MillerRMichelA. Ordinary differential equations, Dover, DE: Dover Publications, 2007.
30.
CarlucciDJacobsonS. Ballistics: theory and design of guns and ammunition, Boca Raton, FL, USA: CRC Press, 2007.
31.
Murphy CH. Free flight motion of symmetric missiles. Technical Report 1216. MD: Ballistic Research Laboratories, Aberdeen Proving Ground, 1963.
32.
Costello M and Anderson D. Effect of internal mass imbalance on the terminal accuracy and stability of a projectile. In: Proceedings of the 1990 AIAA flight mechanics conference, San Diego, CA, pp. 29–31. New York: AIAA.
BrownJChurchillR. Complex variables and applications, 8th ed. Monterey, CA, USA: McGraw-Hill, 2009. Chapter 3.
35.
Fresconi F and Brown T. Very affordable precision projectile system and flight experiments. In: 27th Army Science conference. Orlando, FL, USA, 29 November–2 December 2011.
36.
Dupuis A. Aeroballistic range and wind tunnel tests of the basic finner reference projectile from subsonic to high supersonic velocities. Technical Report. Canada: Defense Research and Development, 2002.
