ECE570 Lecture 14: Qualitative Physics

Transcription

1 ECE570 Lecture 14: Quttve Physcs Jeffrey Mrk Sskd Sch f Eectrc d Cmuter Egeerg F 2017 Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

2 A Physc System Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

3 Mdeg Physc System Dfferet Equts = f () = g() = h() = = ȧ Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

4 Dfferet Equts s Cstrts f g h d/dt = f () = g() = h() = = ȧ Vrbes rge ver fucts frm res (tme) t res. A cstrt such s z = x y mes ( t)[z(t) = x(t) y(t)]. y = ẋ mes tht y s the dervtve f x. Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

5 Numerc Suts s Dfferece Equts f g h d/dt = f () = g() = h() = = ȧ Vrbes rge ver (fte) sequeces f re umbers. A cstrt such s z = x y mes ( )[z = x y ]. y = ẋ mes ( )[x +1 = x + y ] (MVT). Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

6 Ufdg the CSP f g h f g h f g h f g h Vrbes rge ver re umbers. A cstrt such s z = x y mes z = x y. N mre cstrts f the frm y = ẋ. Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

7 Need It Cdts f g h f g h f g h f g h (0) = 0 ( t)(t) = c Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

8 Prbems D t kw wht the fucts f, g, d h re. Mght hve y rt frmt,.e. tht they re mtcy cresg. D t kw wht the t cdt cstt c s. Mght hve y rt frmt,.e. tht t s stve. C we st swer quests ke: C the tk f u? W t f u? C t verfw? C t emty? C t rech equbrum? C t scte? Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

9 Qutty Sces Isted f rgg ver re umbers, vrbes w rge ver fte set f quttve vues. Quttve vues re ether dmrks r rges (e tervs betwee dmrks). A set f quttve vues s ced qutty sce. {0, (0, fu), fu, (fu, ), } ȧ {, (, 0), 0, (0, ), } {0, (0, t), t, (t, ), } {0, (0, ), } {0, (0, c), c, (c, ), } Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

10 Quttve Mutct (, 0) 0 (0, ) (, 0) 0 (0, ) Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

11 Quttve Addt + (, 0) 0 (0, ) (, 0) 0 (0, ) Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

12 Quttve Mtc Fucts x (, 0) 0 (0, ) M + (x) x (, 0) 0 (0, ) M (x) Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

13 Quttve CSP M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

14 Quttve Tme Tme s s rereseted wth qutty sce. Ldmrk quttve tme vues re ced stts. Rge quttve tme vues re ced tervs. Quttes re dexed by quttve tme: x t, ẋ t,.... Predctes: INSTANT(t), INTERVAL(t), LANDMARK(x t ), RANGE(x t ), ADJACENT(t, t ), d ADJACENT(x, x ). t s s the strt tme. t f s the fsh tme. Budry cdts: INTERVAL(t s ) d INTERVAL(t f ). Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

15 Cdt I Ctuty Quttes must tke djcet r equ quttve vues t djcet quttve tmes. ( x)( t)( t ){ADJACENT(t, t ) [ADJACENT(x t, x t ) (x t = x t )]} Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

16 Cdt II Ldmrks If qutty tkes dmrk vue durg terv the t must tke tht sme dmrk vue durg the djcet stts. { ( x)( t)( t [INTERVAL(t) LANDMARK(xt ) ADJACENT(t, t ) } )] (x t = x t ) Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

17 Cdt III Sttrty If qutty tkes dmrk vue durg terv the ts quttve dervtve must be zer durg tht terv. ( x)( t) {[INTERVAL(t) LANDMARK(x t )] (ẋ t = 0)} Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

18 Cdt IV Mergg Idetc Adjcet Itervs There ct be terv fwed by stt fwed by terv where qutty chges. { ( t)( t )( t [ADJACENT(t, t ) ) ADJACENT(t, t ) t } > t INTERVAL(t)] ( x) [(x t x t ) (x t x t )] Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

19 Cdt V Quttve Me-Vue Therem The quttve dfferece betwee the quttve vue f qutty t djcet terv d stt must be equ t the quttve dervtve f tht qutty durg tht terv. { ( t)( t )( t [ADJACENT(t, t ) ) ADJACENT(t, t ) t > t INTERVAL(t } )] [(x t = x t + ẋ t ) (x t = x t + ẋ t )] Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20

20 Cdt VI Termt The system ct be quescet excet durg the st terv. ( t) [ (t t f ) ( ẋ)(ẋ 0) ] Sskd (Purdue ECE) ECE570 Lecture 14: Quttve Physcs F / 20