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倒立摆全套资料 word g格式


..

x?0,?1??0,? 2??0, x?0,?1??0,? 2??0, x?0

k 21???

 f2 |  x x?0,? ??0,? ??0, x?0,? ??0,? ??0, x?0
. . . 1 2 1 2

..

k 22???

 f2

 ?1 x?0,? ??0,? ??0, x?0,? ??0,? ??0, x?0
1 2 1 2

|

.

.

.

..

k 23???

|  ? 2 x?0,? ??0,? ??0, x??0,? ??0,? ??0, x??0
. . . 1 2 1 2

 f2

..

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第 6 章 直线两级倒立摆

k 24???

 f2 x
.

|

x?0,?1??0,? 2??0, x?0,?1??0,? 2??0, x?0

.

.

.

..

k 25???

 f2  ??1
.

|

x?0,?1??0,? 2??0, x?0,?1??0,? 2??0, x?0

.

.

.

..

k 26???

 f2  ?? 2
.

|

x?0,?1??0,? 2??0, x?0,?1??0,? 2??0, x?0

.

.

.

..

k 27???

 f2 x
..

|

x?0,?1??0,? 2??0, x?0,?1??0,? 2??0, x?0

.

.

.

..

在 Mathematics 中计算以上各式: (计算文件请参见“GLIP2002建模文件MathematicaFile”中的“L2DIP.nb”文 件。)
PRO 6-1 直线两级倒立摆建模 Mathematics 程序 TM= 1 2 Mcar? x @tD2 ; xpend1= [email protected]? l1? [email protected]θ [email protected]; ypend1= l1? [email protected]θ [email protected]; tpend1= 1ê2? m1? HH?t xpend1L^2+ H?t ypend1L^2L + 1ê2? H1ê 3? m1? l1^2L? θ 1'@tD^2; xpend2= [email protected]? 2? l1? [email protected]θ [email protected]? l2? [email protected]θ [email protected]; ypend2= 2? l1? [email protected]θ [email protected] + l2? [email protected]θ [email protected]; tpend2= 1ê2? m2? HH?t xpend2L^2+ H?t ypend2L^2L + 1ê2? H1ê 3? m2? l2^2L? Hθ 2'@tDL^2; xmass= [email protected]? 2? l1? [email protected]θ [email protected]; ymass= 2? l1? [email protected]θ [email protected]; tmass = ê? 2?ypend1 m3? HH+ ?t m2 xmass + H?t ymass L^2 L; v= m1 ?1 g ? g?L^2 ypend2 + m3? g? ymass;

Simplify @+ vD; lang = TM tpend1+ tpend2+tmass? v;

[email protected]; ldad= ?θ 1'@tD lang; [email protected]; f1= ?t ldad? ?θ [email protected] lang; [email protected]; ldbd= ?θ 2'@tD lang; [email protected]; f2= ?t ldbd? ?θ [email protected] lang; [email protected]; [email protected] 0, f2== 0< add= θ 1''@tD ê.%; bdd= θ 2''@tD ê.%;
,

8θ 1''@tD, θ 2''@tD<D;

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第 6 章 直线两级倒立摆

k11= [email protected] add ê[email protected] → 0 ê. θ [email protected] → 0 ê. θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê.
θ 2'@tD → 0 ê. x''@tD → 0;

k12= ?θ [email protected] add ê. [email protected] → 0 ê. θ [email protected] → 0 ê.θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê.
θ 2'@tD → 0 ê. x''@tD → 0; k13= ?θ [email protected] add ê. [email protected] → 0 ê. θ [email protected] → 0 ê.θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê. θ 2'@tD → 0 ê. x''@tD → 0;

k14= ?x'@tD add ê[email protected] → 0 ê.θ [email protected] → 0 ê. θ [email protected] → 0 ê. x'@tD → 0 ê. a'@tD → 0 ê. θ 2'@tD → 0 ê. x''@tD → 0; k15= ?θ 1'@tD add ê. [email protected] → 0 ê. θ [email protected] → 0 ê.θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê.
θ 2'@tD → 0 ê. x''@tD → 0; k16= ?θ 2'@tD add ê. [email protected] → 0 ê. θ [email protected] → 0 ê.θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê. θ 2'@tD → 0 ê. x''@tD → 0;

k17= ?x''@tD add ê[email protected] → 0 ê. θ [email protected] → 0 ê. θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê. θ 2'@tD → 0 ê. x''@tD → 0; k21= [email protected] bdd ê[email protected] → 0 ê. θ [email protected] → 0 ê. θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê. θ 2'@tD → 0 ê. x''@tD → 0; k22= ?θ [email protected] bdd ê. [email protected] → 0 ê. θ [email protected] → 0 ê.θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê.
θ 2'@tD → 0 ê. x''@tD → 0; k23= ?θ [email protected] bdd ê. [email protected] → 0 ê. θ [email protected] → 0 ê.θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê. θ 2'@tD → 0 ê. x''@tD → 0;

k24= ?x'@tD bdd ê[email protected] → 0 ê. θ [email protected] → 0 ê. θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê. θ 2'@tD → 0 ê. x''@tD → 0; k25= ?θ 1'@tD bdd ê. [email protected] → 0 ê. θ [email protected] → 0 ê.θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê.
θ 2'@tD → 0 ê. x''@tD → 0; k26= ?θ 2'@tD bdd ê. [email protected] → 0 ê. θ [email protected] → 0 ê.θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê. θ 2'@tD → 0 ê. x''@tD → 0;

k27= ?x''@tD bdd ê[email protected] → 0 ê. θ [email protected] → 0 ê. θ [email protected] → 0 ê. x'@tD → 0 ê. θ 1'@tD → 0 ê. θ 2'@tD → 0 ê. x''@tD → 0; [email protected] [email protected] S[email protected] [email protected] [email protected] Simplify @k27 D = 0.13; m3= 0.236; l1 = 0.0775; l2 = 0.25; g = 9.8; m1= 0.05; m2 k12 k13 k17 k22 k23 k27

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第 6 章 直线两级倒立摆

因其余各项为 0,所以这里仅列举了 k12、k13、k17、k22、k23、k27 等 7 项,得到结果如下: k12??? 3g (m1?? 2(m2?? m3)) (4m1?? 3(m2?? 4m3))l1 9 gm2 2(4m1?? 3(m2?? 4m3))l1 3(2m1?? m2?4m3) 2(4m1?? 3(m2?? 4m3))l1 9g (m1?? 2(m2?? m3)) 2(4m1?? 3(m2?? 4m3))l 2 3g (m1?? 3(m2?? m3)) (4m1?? 3(m2?? 4m3))l 2 3(m1?l 2m3) 2(4m1?? 3(m2?? 4m3))l 2
? ?0 x ? ?? ?? 0 0 0 0 0 0 0 21.62 39.45

? 86.69

k13???

?? 21.62

k17???

? 6.64

k 22???

?? 40.31

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