·ÖÎöÁ¦Ñ§Ñо¿½øÕ¹

Ŀ¼ Ç°ÑÔ **Õ ·ÖÎöÁ¦Ñ§½øÕ¹ 1 1.1 ·ÖÎöÁ¦Ñ§µÄ½ü´ú·¢Õ¹ 1 1.2 ¾­µäÁ¦Ñ§´ÓÅ£¶Ùµ½²®¿Ë»ô·ò 9 1.3 Öйú·ÖÎöÁ¦Ñ§40Äê 17 1.4 ¾­µäÁ¦Ñ§µÄÀúÊ·¹±Ï×ÓëÆôʾ 24 µÚ¶þÕ ·ÇÍêÕûÁ¦Ñ§½øÕ¹ 41 2.1 ·ÇÍêÕûϵͳÁ¦Ñ§µÄÀúÊ·ÓëÏÖ×´ 41 2.2 ·ÇÍêÕûϵͳÁ¦Ñ§»ý·Ö·½·¨µÄijЩ½øÕ¹ 47 2.3 ·ÇÍêÕûϵͳÎȶ¨ÐÔµÄÈô¸É½øÕ¹ 63 2.4 Nonholonomic mechanics 80 2.5 ·ÇÍêÕûÔ¼Êøϵͳ¼¸ºÎ¶¯Á¦Ñ§Ñо¿½øÕ¹£ºLagrangeÀíÂÛ¼°ÆäËû 139 µÚÈýÕ BirkhoffÁ¦Ñ§½øÕ¹ 16¿ª9 3.1 Birkhoffϵͳ¶¯Á¦Ñ§µÄÑо¿½øÕ¹ 16¿ª9 3.2 On the Birkhoffan mechanics 180 µÚËÄÕ ¶Ô³ÆÐÔÓëÊغãÁ¿½øÕ¹ 200 4.1 ¹ØÓÚÁ¦Ñ§ÏµÍ³µÄ¶Ô³ÆÐÔÓë²»±äÁ¿ 200 4.2 Symmetries and conserved quantities of constrained mechanical systems 216¿ª µÚÎåÕ ±ä·ÖÔ­Àí½øÕ¹ 258 5.1 ¹ØÓÚHamiltonÔ­Àí 258 5.2 ¹ØÓÚGaussÔ­Àí 270