But v_j^2=V^2+(v_j-V)^2 is absurd and not needed

But v_j^2=V^2+(v_j-V)^2 is absurd and not needed

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送交者: gyro 于 2009-10-29, 00:57:54:

回答: 速度为v_j的质点j的能量是v_j^2,质心速度是V,所以j的能量为v_j^2=V^2+(v_j-V)^2。由 Palmetto 于 2009-10-29, 00:50:19:

for jth particle alone, V^2+(v_j-V)^2 has no clear meaning. For the system,

sum_j m_j v_j^2/2= MV^2/2 + sum_j m_j(v_j-V)^2/2,

is again an identity and does not require v_j^2=V^2+(v_j-V)^2. This is because MV=sum_j m_j v_j, by definition.

另外，如果不对时间平均的话，v_j^2是个变数，非守恒。 - Palmetto (75 bytes) 2009-10-29, 02:04:48 (378216)
- Who said m_j v_j^2 is conserved? - gyro (363 bytes) 2009-10-29, 02:12:50 (378220)
  - 咱们不是在讨论用能量守恒证明动量守恒吗？不守恒如何证明？ - Palmetto (22 bytes) 2009-10-29, 02:46:47 (378228)
你这样，不是提前用了动量守恒吗？ (无内容) - Palmetto (0 bytes) 2009-10-29, 01:56:17 (378212)
- I never take the Berkeley "proof" seriously - gyro (151 bytes) 2009-10-29, 02:05:00 (378217)
  - 仅仅定义是不够的，因为v_j是变数，它们的合可能也是。 (无内容) - Palmetto (0 bytes) 2009-10-29, 02:43:54 (378225)
v_j^2=V^2+(v_j-V)^2的成立，必须对时间平均。 (无内容) - Palmetto (0 bytes) 2009-10-29, 01:16:10 (378199)
别弄那么多点了，只考虑用弹簧连接的两个球，两球振动v=a*coswt，质心速度为V。 - Palmetto (36 bytes) 2009-10-29, 01:08:03 (378196)