对于微分方程 [tex=9.571x1.571]xqYXgtAevH5Be4RuJxpQsYYsLyzzHqtyYdxDjLatGiTSouyRYUxAd3LrtxbSdYRMjBOYMUyivF9H2UofEUqy3w==[/tex] 验证该方程不是恰当方程
对于微分方程 [tex=9.571x1.571]xqYXgtAevH5Be4RuJxpQsYYsLyzzHqtyYdxDjLatGiTSouyRYUxAd3LrtxbSdYRMjBOYMUyivF9H2UofEUqy3w==[/tex] 验证该方程不是恰当方程
求函数[tex=9.571x1.571]apbD0nRmlcdVZi5bj1fGfFnEk1XQpWZJehT+sYItVd4Fk+oX14reG5d1J4e3R4/9[/tex][tex=5.786x2.5]YHwiPugA06KcPVx+cUYIeakNgu/KTr77Yx6QhGSIqgg3vawn9kNKnqpPK/mfQ4AQ[/tex]的极值。
求函数[tex=9.571x1.571]apbD0nRmlcdVZi5bj1fGfFnEk1XQpWZJehT+sYItVd4Fk+oX14reG5d1J4e3R4/9[/tex][tex=5.786x2.5]YHwiPugA06KcPVx+cUYIeakNgu/KTr77Yx6QhGSIqgg3vawn9kNKnqpPK/mfQ4AQ[/tex]的极值。
图 [tex=0.5x1.0]oYgVDn+QZqcDCRxqEZwM2A==[/tex] 所示结构,单元[tex=3.429x1.286]+7TdJK85hLvn8SJ3m1S+Xw==[/tex]的固端弯矩列为 [tex=14.786x1.571]+L/t8MXaGFoWiRt4BP7RRkxvzeIppU/DGGFkYSEcRw3kvLvw7ZDaSR6F+d/gxiDcg5viqYt5X24ISYuBuMMpnVyeYjpkVY66bR49xV0DkM7YnM1V/IU1FesL7lKe18QHeBH3Kl1IWvddDDX1svI9xQ==[/tex] 则等效结点荷载列阵为。[img=356x167]179cc96e65c84fb.png[/img] 未知类型:{'options': ['[tex=10.214x1.643]3uFeplA1M1mlL2JJ6qFDKT73bT9ixBsm437RYI3BYhNMyutkpTN9KoJG8zUUk7k6dB516y1Y4QO3s87qWYU5psTLtY7JCkhRoXHPL2CZoJdYVYX57J7cyciYof/2Fh/g[/tex]', '[tex=9.571x1.571]Wz6FUy6gMShWKR6vXpXZufkRYrBSDCWGYmt/cnUiIai20EZY+Hxu6CLDdQXxD51O5z0c4J/CzO7nsBCki0bZmTYwemla49xJKGUFV5YvytvkQIuing1VfWw3HoiX0R6p[/tex]', '[tex=9.571x1.571]Wz6FUy6gMShWKR6vXpXZufkRYrBSDCWGYmt/cnUiIagRhPY9neMcesV2adBxOwua7R52cHho7bDCORdUvOzvRvoCcnInbPcql1wOBLggQPQcda2zZ9vc04CkCYwEc8UM[/tex]', '[tex=9.571x1.571]Wz6FUy6gMShWKR6vXpXZufkRYrBSDCWGYmt/cnUiIagRhPY9neMcesV2adBxOwuaes18TL5V3J/lq6aUvyTT149sZZMk8Je10CFP9V/BNKxXmOIdI8p72p/dvyyp+vd2[/tex]'], 'type': 102}
图 [tex=0.5x1.0]oYgVDn+QZqcDCRxqEZwM2A==[/tex] 所示结构,单元[tex=3.429x1.286]+7TdJK85hLvn8SJ3m1S+Xw==[/tex]的固端弯矩列为 [tex=14.786x1.571]+L/t8MXaGFoWiRt4BP7RRkxvzeIppU/DGGFkYSEcRw3kvLvw7ZDaSR6F+d/gxiDcg5viqYt5X24ISYuBuMMpnVyeYjpkVY66bR49xV0DkM7YnM1V/IU1FesL7lKe18QHeBH3Kl1IWvddDDX1svI9xQ==[/tex] 则等效结点荷载列阵为。[img=356x167]179cc96e65c84fb.png[/img] 未知类型:{'options': ['[tex=10.214x1.643]3uFeplA1M1mlL2JJ6qFDKT73bT9ixBsm437RYI3BYhNMyutkpTN9KoJG8zUUk7k6dB516y1Y4QO3s87qWYU5psTLtY7JCkhRoXHPL2CZoJdYVYX57J7cyciYof/2Fh/g[/tex]', '[tex=9.571x1.571]Wz6FUy6gMShWKR6vXpXZufkRYrBSDCWGYmt/cnUiIai20EZY+Hxu6CLDdQXxD51O5z0c4J/CzO7nsBCki0bZmTYwemla49xJKGUFV5YvytvkQIuing1VfWw3HoiX0R6p[/tex]', '[tex=9.571x1.571]Wz6FUy6gMShWKR6vXpXZufkRYrBSDCWGYmt/cnUiIagRhPY9neMcesV2adBxOwua7R52cHho7bDCORdUvOzvRvoCcnInbPcql1wOBLggQPQcda2zZ9vc04CkCYwEc8UM[/tex]', '[tex=9.571x1.571]Wz6FUy6gMShWKR6vXpXZufkRYrBSDCWGYmt/cnUiIagRhPY9neMcesV2adBxOwuaes18TL5V3J/lq6aUvyTT149sZZMk8Je10CFP9V/BNKxXmOIdI8p72p/dvyyp+vd2[/tex]'], 'type': 102}
若无限长的半径为a的圆柱体中电流密度分布函数[tex=9.571x1.571]sdktR4/vZFe2BIP7otGGYO4rXGcO4YLlp6iOrcBUL4CDXdVS0RQ/HysO7O5PzxVwkWugasHBgJAsJH2Np37nog==[/tex] ,试求圆柱内外的磁感应强度。
若无限长的半径为a的圆柱体中电流密度分布函数[tex=9.571x1.571]sdktR4/vZFe2BIP7otGGYO4rXGcO4YLlp6iOrcBUL4CDXdVS0RQ/HysO7O5PzxVwkWugasHBgJAsJH2Np37nog==[/tex] ,试求圆柱内外的磁感应强度。
对于微分方程 [tex=9.571x1.571]xqYXgtAevH5Be4RuJxpQsYYsLyzzHqtyYdxDjLatGiTSouyRYUxAd3LrtxbSdYRMjBOYMUyivF9H2UofEUqy3w==[/tex] 在方程两边乘以 [tex=1.0x1.214]1dVN4VU1CcV58EijxscpUA==[/tex] 后, 确定 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 的值使之成为恰当方程
对于微分方程 [tex=9.571x1.571]xqYXgtAevH5Be4RuJxpQsYYsLyzzHqtyYdxDjLatGiTSouyRYUxAd3LrtxbSdYRMjBOYMUyivF9H2UofEUqy3w==[/tex] 在方程两边乘以 [tex=1.0x1.214]1dVN4VU1CcV58EijxscpUA==[/tex] 后, 确定 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 的值使之成为恰当方程
若C为常数,A及k为常矢量,试证:①[tex=6.214x1.214]S6hpMdq+c0xUUj2qviqxPvTKZE23IVtA8eHted4k4srsQ6Y1YGDyZVXumxj/xgZ9[/tex]②[tex=9.571x1.571]+uqEelBTaZpp8y2SsBkhvGgGaaLwNq+0KgFbzbs4Gq0/RW0A0oUSJHdzZdJp7NLw0dcgBrwWv/yS2884ojiNrFixJ6515aQ+8C1IwryYe+U=[/tex]③[tex=10.571x1.571]kBCMbqQHHZb2fcr3oDOco0DNJuGe4WALdADZ6k9MCYVPPGcUI2jDknNv3/xsr3WyDwc/SNuAJ+BxzAV+kxFQjfV/EbKVVeyMRcIMC6alK5s=[/tex]
若C为常数,A及k为常矢量,试证:①[tex=6.214x1.214]S6hpMdq+c0xUUj2qviqxPvTKZE23IVtA8eHted4k4srsQ6Y1YGDyZVXumxj/xgZ9[/tex]②[tex=9.571x1.571]+uqEelBTaZpp8y2SsBkhvGgGaaLwNq+0KgFbzbs4Gq0/RW0A0oUSJHdzZdJp7NLw0dcgBrwWv/yS2884ojiNrFixJ6515aQ+8C1IwryYe+U=[/tex]③[tex=10.571x1.571]kBCMbqQHHZb2fcr3oDOco0DNJuGe4WALdADZ6k9MCYVPPGcUI2jDknNv3/xsr3WyDwc/SNuAJ+BxzAV+kxFQjfV/EbKVVeyMRcIMC6alK5s=[/tex]
设 [tex=15.214x2.786]fGBrBmik4XPm0BiWuJqpSu7wihJxFsUbuSfSeMuTnlCd94HPy94CjACfMQ2kVoypm2r8rx89nzr9cH+DadQiGTt0pu3kmSWA4Vp+DabuYA6hKZEqdDP8IKCYaIQ0pUjPJ2v9d9ObUNvTTlmcZuJRLyEuajSAYaXapiFdi0Tldp7RcfJ6FgmukSwAWT+/DppS[/tex] . 证明 [tex=18.286x2.286]9tDK5mf6vAM929c4ddDggyupQ+VJ2WbTzSM8LVF3npw1AAEStzYq6rGEeUYUZw3MDzlR1TIyiHzclDLYYwe+Fl5HNmTMQ8rptqRWW2CA5O8etKtig8xz8ym3QZ//GpL5d3NS59j80ZSpXhNNDaxuTWjk6S6/JrS/rDCqzTMTHik=[/tex],其中 [tex=9.571x1.571]Ns9WDnm5mKiE4wzKiOtEBb+9lf5BO4EdM1L2VmaiihcOHROwptd6R4FfRxt+Kcye35tOjaXS+xzhVJgBODftGQ==[/tex],[tex=1.786x2.214]t52cQAsFAmSV6XlZMXYYyEOVetg7MVmsPbCV8R/b9E4=[/tex] 表示 [tex=0.857x2.143]SHy24wQWjYBVVxFBAkTfJA==[/tex] 的整数部分.
设 [tex=15.214x2.786]fGBrBmik4XPm0BiWuJqpSu7wihJxFsUbuSfSeMuTnlCd94HPy94CjACfMQ2kVoypm2r8rx89nzr9cH+DadQiGTt0pu3kmSWA4Vp+DabuYA6hKZEqdDP8IKCYaIQ0pUjPJ2v9d9ObUNvTTlmcZuJRLyEuajSAYaXapiFdi0Tldp7RcfJ6FgmukSwAWT+/DppS[/tex] . 证明 [tex=18.286x2.286]9tDK5mf6vAM929c4ddDggyupQ+VJ2WbTzSM8LVF3npw1AAEStzYq6rGEeUYUZw3MDzlR1TIyiHzclDLYYwe+Fl5HNmTMQ8rptqRWW2CA5O8etKtig8xz8ym3QZ//GpL5d3NS59j80ZSpXhNNDaxuTWjk6S6/JrS/rDCqzTMTHik=[/tex],其中 [tex=9.571x1.571]Ns9WDnm5mKiE4wzKiOtEBb+9lf5BO4EdM1L2VmaiihcOHROwptd6R4FfRxt+Kcye35tOjaXS+xzhVJgBODftGQ==[/tex],[tex=1.786x2.214]t52cQAsFAmSV6XlZMXYYyEOVetg7MVmsPbCV8R/b9E4=[/tex] 表示 [tex=0.857x2.143]SHy24wQWjYBVVxFBAkTfJA==[/tex] 的整数部分.
给定方程 [tex=9.571x1.571]rjzw0bBUODiY66l+Mq83xASYQBFLpSxKUlCVFG2HCWWxj9nlhTtIQlVnCGKeBagZskQiAVPPVe4dqmuOQbPexg==[/tex]证明 [tex=9.357x2.929]+sfv9fbaljqgKDIK5JrU9RyBATOPy9ytuureroYqKHxDMj/2822HztoO7LhkOK8x6vPgC9+nASLQULO0//8HUH4tis7BrPENS1t42f/RVno04ZH2nvYZOOzgrI9QeKak[/tex], 并将方程化为以 [tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex]为因变量,以 [tex=0.5x1.0]yBR4oiFoTexGaFalQ7m8kg==[/tex]为自变量的形式;
给定方程 [tex=9.571x1.571]rjzw0bBUODiY66l+Mq83xASYQBFLpSxKUlCVFG2HCWWxj9nlhTtIQlVnCGKeBagZskQiAVPPVe4dqmuOQbPexg==[/tex]证明 [tex=9.357x2.929]+sfv9fbaljqgKDIK5JrU9RyBATOPy9ytuureroYqKHxDMj/2822HztoO7LhkOK8x6vPgC9+nASLQULO0//8HUH4tis7BrPENS1t42f/RVno04ZH2nvYZOOzgrI9QeKak[/tex], 并将方程化为以 [tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex]为因变量,以 [tex=0.5x1.0]yBR4oiFoTexGaFalQ7m8kg==[/tex]为自变量的形式;
设 [tex=9.571x1.571]J9rDo0JU0mK8uFkf5jXgkGj0whRGBkHvZ5fDiJ7jo+P9/KBeA/Vds2rlyYN2je/B[/tex][p=align:center][tex=11.857x2.786]aVYX6/IOZGjYjrxJLwfiaz4NPHBVh8h7mttP6uhPOfHJLrwFvon6MewSAWA0wrqEGT0uR06viCWuQ5D0EZQM7OvimmS6O88aORnngoL5sUrwZjZee55TQdEJeczQVQoj79VCOfDVsDDTenJFc9Ls/A==[/tex]证明 [tex=0.786x1.0]AE39d9jt5lmaK/QknwwnQQ==[/tex] 与[tex=0.857x1.0]aPLFPHMGSKDwulHSwLWugg==[/tex]关于加法运算是同构的。
设 [tex=9.571x1.571]J9rDo0JU0mK8uFkf5jXgkGj0whRGBkHvZ5fDiJ7jo+P9/KBeA/Vds2rlyYN2je/B[/tex][p=align:center][tex=11.857x2.786]aVYX6/IOZGjYjrxJLwfiaz4NPHBVh8h7mttP6uhPOfHJLrwFvon6MewSAWA0wrqEGT0uR06viCWuQ5D0EZQM7OvimmS6O88aORnngoL5sUrwZjZee55TQdEJeczQVQoj79VCOfDVsDDTenJFc9Ls/A==[/tex]证明 [tex=0.786x1.0]AE39d9jt5lmaK/QknwwnQQ==[/tex] 与[tex=0.857x1.0]aPLFPHMGSKDwulHSwLWugg==[/tex]关于加法运算是同构的。
设系统的拉格朗日函数为[tex=16.0x2.786]nyi+AmRRGBNZ2tlVUCeOlsA2jnAwXtm6/tr6605HtuMQ/S7KCxb99PBEMyCGdS+JlHkGqtHAMUJNXgEELFxXTAmlbcqoToqAN+gBPw2wJDxeEDg35bYxxLnO80csSviOEUfatsw1QrnrOXRS+LnEB3TqV6Ew/tmqNawCyHBxykc=[/tex]并设生成函数为[tex=9.571x1.571]c+Lb7f9MMJ1P0fGx+/7Do5vJQcX+JBUNoZZnkc92OWAkf+yJR5oUVuCm2XFX01VxWWJ/ZoQFO04OnVQXV++MOg==[/tex], 试用哈密顿 - 雅可比方程求系统的运动方程.
设系统的拉格朗日函数为[tex=16.0x2.786]nyi+AmRRGBNZ2tlVUCeOlsA2jnAwXtm6/tr6605HtuMQ/S7KCxb99PBEMyCGdS+JlHkGqtHAMUJNXgEELFxXTAmlbcqoToqAN+gBPw2wJDxeEDg35bYxxLnO80csSviOEUfatsw1QrnrOXRS+LnEB3TqV6Ew/tmqNawCyHBxykc=[/tex]并设生成函数为[tex=9.571x1.571]c+Lb7f9MMJ1P0fGx+/7Do5vJQcX+JBUNoZZnkc92OWAkf+yJR5oUVuCm2XFX01VxWWJ/ZoQFO04OnVQXV++MOg==[/tex], 试用哈密顿 - 雅可比方程求系统的运动方程.