理论力学课后答案第五章（周衍柏）

有

??LH?p??

?5?7?5p??p?2???p???m?c?b?mg?c?b?cos????22?7m?c?b??10?7m?c?b?? 5p?2??mg?c?b?cos?214m?c?b?2?4?根据正则方程

???p?H?mg?c?b?sin?④ ?????对式两边求时间导得：

5p??H⑤ ?2?p?7m?c?b???????5p7m?c?b?2?5mg?c?b?sin?7m?c?b?2?5gsin?

7?c?b?故小球球心切向加速度

???5gsin? a??c?b??7

5.25解根据第二章§2.3的公式有：

??i????yipiz?zipiy???i?ziyJx??mi?yizi?1i?1?nn??i?xiz?i????zipix?xipiz??① Jy??mi?zixi?1i?1?nn??i?yix?i????xipiy?yipix??Jz??mi?xiyi?1i?1?nn根据泊松括号的定义：

????,??????s????????p??q?i?1??q??p???② ???所以

?J同理可知：

x,Jy???i?1?n?Jx?Jx?Jx?Jx??q??p??p??q??

?J由②得：

y,Jy?0, ?Jz,jz??0

??Jnx,Jy???Jx?Jy?Jx?Jy?????q?p??p?qi?1?????s? ??????Jx?Jy?Jx?Jy???Jx?Jy?Jx?Jy???Jx?Jy?Jx?Jy??????????x?p??p?x?????y?p??p?y?????z?p??p?z???i?1?ixixi?iyiyi?izizi???i?i??i? ???xipiy?yipix??Jzi?1n同理可得：

?Jy,Jz?Jx, ?Jz,Jx??Jy

?5.26解 由题5.25可知Jx,Jy,Jz的表达式 因为

?py?py?py?p??p??1,?0;?0,?0,?0 ?p??p??x?y?z故

???Jx?py?Jx?pyJx,py?????q?p??p?qi?1??????s? ???n??yp?zp??Jxiiziiy????y?yii?1

??piz?pzi?1n同理可求得：

?n??xp?yp?n?JziiyiixJz,py??????pix??px

?y?yii?1i?1??J,p????Jyyyy?0