San José State University Aerospace Engineering AE 138 Vector-Based Dynamics for Aerospace Applications, Fall 2016

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1 San José Stat Univrsity Arospac Enginring AE 138 Vctor-Basd Dynamics for Arospac Applications, Fall 2016 Instructor: Offic Location: Offic Hours: Class Days/Tim: Classroom: Prof. J.M. Huntr E272F MW 10:30 am 1:15 pm M 4:30 pm 6:00 pm MW 1:30 2:45pm E164 Prrquisits: Grad of C or bttr in MATH 32 Co-rquisit: Class Wbsit AE112 Undr th courss tab, slct this cours Onlin Courss Usually this class will mt in prson in Enginring 164. Somtims, howvr, th class will mt onlin, using a WbEx link. In ths cass, I will announc th onlin schdul ahad of tim and post th link on Canvas. Cours Dscription Vctor mchanics of thr dgr-of-frdom particl motion. Particl kinmatics, rfrnc frams and rotational rlativ motion. Two dgr-of-frdom rigid body motion, momnts/products of inrtia. Particl & rigid body quations of motion and numrical tim historis. Cours Goals 1. To provid a fundamntal knowldg of vctor dynamics. 2. To stablish th basics of rfrnc fram mchanics and rlativ motion. 3. To provid th fundamntals of particl kinmatics of using Nwtonian mthods. 4. To writ thr-dimnsional quations of motion using vctor mchanics. 5. To undrstand th influnc of momnts/products of inrtia on rigid body rotational motion. 6. To dvlop physical intuition about dynamic systms by xamining th connction btwn th diffrntial quations (quations of motion) and thir tim history solution. Cours Larning Outcoms 1. Combin and solv for vctors using th oprations of vctor algbra. 2. Find ara using vctor algbra. 3. St up basis vctors and us thm to xprss and solv for particl position. 4. St up a dirction cosin matrix rlating th planar orintation of two rfrnc frams. Vctor-basd Dynamics for Arospac Applications, AE 138, Fall 2016 Pag 1 of 5

2 5. Exprss and rsolv vctors into rfrnc frams rlatd by dirction cosin matrics. 6. Diffrntiat scalars; diffrntiat vctors in arbitrary rfrnc frams. 7. Exprss angular vlocity/acclration and rlat ths concpts to th dirction cosin matrix. 8. Solv kinmatic (position/vlocity/acclration) problms whn multipl rfrnc frams ar involvd. 9. Exprss particl and rigid body constraints for rolling and sliding (slipping) situations. 10. Calculat mass cntr of a systm of particls and of a rigid body. 11. Calculat rigid body mass momnts/products of inrtia (mass proprtis). Intuitivly undrstand th rlationship btwn mass proprtis and rigid body motion. 12. Writ th linar/angular momntum vctors of a dynamic systm. 13. Inrtially diffrntiat linar/angular momntum vctors, st thm qual to applid forcs/momnts and thrby writ th quations of motion of th systm. 14. Writ th total kintic nrgy and us it to solv for th motion/raction forcs, tc. of a dynamic systm. 15. Us MotionGnsis to modl th quations of motion of a dynamic systm. Rquird Txts/Radings Txtbook Mitiguy: Dynamics of mchanical, Arospac and Biomchanical Systms, MotionGnsis, Inc. Othr Radings Hibblr: Enginring Mchanics and Dynamics Grnwood: Principls of Dynamics Kan: Dynamics Thomson: Introduction to Spac Dynamics Andrson: Introduction to Flight Cours Rquirmnts and Assignmnts Homwork 15% Projct 25% Two Hour Exams 40% Final Exam 20% Rading assignmnts will b postd for most classs and should b compltd bfor coming to class. Homwork problms will b assignd vry wk or two. Ths homwork sts ar ssntial to your undrstanding. Allow 8 10 hours pr wk for homwork. Oftn w will work problms in groups during th class priod, somtims for crdit, somtims not. As homwork is gradd and rturnd to you, I will post th solutions on Canvas and work slctd problms on th board. If thr is a particular problm that you would lik to s workd out, plas lt m know and I will b sur to mak tim to do this. Final Examination or Evaluation A comprhnsiv writtn final xam will b givn on Thursday, Dcmbr 15, 12:15 2:30pm, in Enginring 164. Grading Information Problm grads ar basd on: i concptual undrstanding (i.., idntifying th corrct physical principl or law of motion), ii stting up th problm quations, and Vctor-basd Dynamics for Arospac Applications, AE 138, Fall 2016 Pag 2 of 5

3 iii solving th problm for a numrical or symbolic xprssion. Two old xam problms ar shown blow, with partial crdit indicatd. (25 pt) An aircraft, particl Q, travls ovrhad at constant altitud, h, and constant horizontal vlocity, v. A radar tracks th aircraft so that b x is always pointd toward th aircraft. r = h. Nwtonian rfrnc fram N is fixd in th ground. Rfrnc fram B is fixd in th radar and rotats with it. This problm happns ntirly in th vrtical plan. (A) Dtrmin th angular vlocity, θ, and th angular acclration, θ, of th radar in trms of v, r(t) and (t). (B) Evaluat θ and θ at th point of closst approach of th airplan to th radar. At this point, = 0 and (C) Hint: Writ two xprssions for N v Q and quat thm. Q v h r Partial Crdit (10 pt) Corrctly writing th xprssion for N p Q and diffrntiating to find N v Q (5 pt) Writing a scond xprssion for N v Q from th problm statmnt (5 pt) Equating th scalar componnts of N v Q and solving for θ and θ (5 pt) Evaluating θ and θ at PCA (25 pt) A satllit (particl Q of mass m) is in an lliptical orbit around th Earth. Th position of Q in N is a function of r and as shown, whr r = r(t) and = (t). Th only forc applid to th particl is th gravitational forc: F Q G m m E r 2 r Vctor-basd Dynamics for Arospac Applications, AE 138, Fall 2016 Pag 3 of 5

4 whr m E = mass of th Earth and G = univrsal gravitational constant. Satllit rfrnc fram, S, consists of r, along radial lin r; which is prpndicular to r in th orbital plan; and z = r x. Writ th quations of motion of th particl, Q. r r Q Earth n y n x Partial Crdit (10 pt) Rcognizing that th Goldn Rul vrsion of Nwton s Scond Law of Motion is th corrct principl (5 pt) Writing th xprssion for N p Q (5 pt) Diffrntiating N p Q to obtain N v Q (5 pt) Using th applid forc to writ th quations of motion; taking th dot product with th unit vctors to obtain scalar quations Dtrmination of Grads Grading Scal: % A+; % A; % A-; % B+; % B; % B-; % C+; % C; % C-; % D+; % D; % D-; < 59.9% F. All xams must b takn to rciv a passing grad. Univrsity Policis Pr Univrsity Policy S16-9, univrsity-wid policy information rlvant to all courss, such as acadmic intgrity, accommodations, tc. will b availabl on Offic of Graduat and Undrgraduat Programs Syllabus Information wb pag at AE Dpartmnt and SJSU policis ar also postd at Vctor-basd Dynamics for Arospac Applications, AE 138, Fall 2016 Pag 4 of 5

5 AE 138 Vctor-basd Dynamics for Arospac Enginring Fall 2016 Cours Schdul Cours Schdul Wk Dat Topics, Radings, Assignmnts, Dadlins 1 8/31 Class Ovrviw 2 9/5 & 9/7 Vctor dynamics rviw 3 9/12 & 9/14 Position vctors and vctor gomtry 4 9/19 & 9/21 Vctor basis 5 9/26 & 9/28 Dirction cosin matrics 6 10/3 & 10/5 Vctor diffrntiation and intgration 7 10/10 & 10/ /17 & 10/ /24 & 10/ /31 & 11/2 Angular vlocity & angular acclration Points: Vlocity and acclration Constraints Particls 11 11/7 & 11/9 Mass, cntr of mass, cntroid 12 11/14 & 11/16 Momnts/Products of inrtia 13 11/21 Inrtia proprtis 14 11/28 & 11/30 Rigid Bodis, forc and momntum 15 12/5 & 12/7 Forc, impuls, and rsultant Momnts and torqu Equations of motion Final Exam Thursday, Dcmbr 15 ENGR 164 at 12:15 pm 2:30 pm Vctor-basd Dynamics for Arospac Applications, AE 138, Fall 2016 Pag 5 of 5

Content Skills Assessments Lessons. Identify, classify, and apply properties of negative and positive angles.

Content Skills Assessments Lessons. Identify, classify, and apply properties of negative and positive angles. Tachr: CORE TRIGONOMETRY Yar: 2012-13 Cours: TRIGONOMETRY Month: All Months S p t m b r Angls Essntial Qustions Can I idntify draw ngativ positiv angls in stard position? Do I hav a working knowldg of