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User:CaffeineP/数学式的推导(表格形式)

维基百科，自由的百科全书

另见用户:CaffeineP/质点力学。

r + * * *
x y z
i j k
v d/dt d/dt + + + + +
r + * * * d/dt * + * * + * * + * 0 * d/dt i
x d/dt x x d/dt x x d/dt x
i i d/dt i i 0 i x
x y z d/dt * + * * + * * + * 0 * d/dt j
y d/dt y y d/dt y y d/dt y
j j d/dt j j 0 j y
i j k d/dt * + * * + * * + * 0 * d/dt k
z d/dt z z d/dt z z d/dt z
k k d/dt k k 0 k z
p * m v * m d/dt * m d/dt * m + * m + * m + * m + * m + + * * *
r + * * * d/dt * + * * + * * + * 0 * d/dt i m m m
x d/dt x x d/dt x x d/dt x
i i d/dt i i 0 i x
x y z d/dt * + * * + * * + * 0 * d/dt j d/dt x d/dt x d/dt x
y d/dt y y d/dt y y d/dt y
j j d/dt j j 0 j y
i j k d/dt * + * * + * * + * 0 * d/dt k i i i
z d/dt z z d/dt z z d/dt z
k k d/dt k k 0 k z
a d/dt v d/dt d/dt d/dt d/dt d/dt + d/dt + d/dt + d/dt + d/dt + + d/dt d/dt d/dt + + + + + + + + + + + + + * * *
r + * * * d/dt * + * * + * * + * 0 * d/dt i * d/dt i * d/dt j * d/dt k * d/dt i * d/dt j * d/dt k * d^2/dt^2 i * d^2/dt^2 j * d^2/dt^2 k * d^2/dt^2 i * d^2/dt^2 j * d^2/dt^2 k d^2/dt^2 x d^2/dt^2 y d^2/dt^2 z
x d/dt x x d/dt x x d/dt x
i i d/dt i i 0 i x
x y z d/dt * + * * + * * + * 0 * d/dt j d/dt x d/dt y d/dt z x y z x y z
y d/dt y y d/dt y y d/dt y
j j d/dt j j 0 j y x y z * d/dt d/dt * d/dt d/dt * d/dt d/dt * d/dt 0 * d/dt 0 * d/dt 0 0 0 0 i j k
i j k d/dt * + * * + * * + * 0 * d/dt k
z d/dt z z d/dt z z d/dt z x i y j z k x y z
k k d/dt k k 0 k z
F * * * * * * * * * * * * * * +
m m m m m m m m m m m m m m * m d^2/dt^2 i
a d/dt v d/dt d/dt d/dt d/dt d/dt + d/dt + d/dt + d/dt + d/dt + + d/dt d/dt d/dt + + + + + + + + + + + + + * * *
r + * * * d/dt * + * * + * * + * 0 * d/dt i * d/dt i * d/dt j * d/dt k * d/dt i * d/dt j * d/dt k * d^2/dt^2 i * d^2/dt^2 j * d^2/dt^2 k * d^2/dt^2 i * d^2/dt^2 j * d^2/dt^2 k d^2/dt^2 x d^2/dt^2 y d^2/dt^2 z x
x d/dt x x d/dt x x d/dt x * m d^2/dt^2 j
i i d/dt i i 0 i x
x y z d/dt * + * * + * * + * 0 * d/dt j d/dt x d/dt y d/dt z x y z x y z y
y d/dt y y d/dt y y d/dt y
j j d/dt j j 0 j y x y z * d/dt d/dt * d/dt d/dt * d/dt d/dt * d/dt 0 * d/dt 0 * d/dt 0 0 0 0 i j k * m d^2/dt^2 k
i j k d/dt * + * * + * * + * 0 * d/dt k
z d/dt z z d/dt z z d/dt z x i y j z k x y z z
k k d/dt k k 0 k z
ri + * * *
xi yi zi
i j k
vi d/dt d/dt + + + + +
ri + * * * d/dt * + * * + * * + * 0 * d/dt i
xi d/dt xi xi d/dt xi xi d/dt xi
i i d/dt i i 0 i xi
xi yi zi d/dt * + * * + * * + * 0 * d/dt j
yi d/dt yi yi d/dt yi yi d/dt yi
j j d/dt j j 0 j yi
i j k d/dt * + * * + * * + * 0 * d/dt k
zi d/dt zi zi d/dt zi zi d/dt zi
k k d/dt k k 0 k zi
pi * mi vi * mi d/dt * mi d/dt * mi + * mi + * mi + * mi + * mi + + * * *
ri + * * * d/dt * + * * + * * + * 0 * d/dt i mi mi mi
xi d/dt xi xi d/dt xi xi d/dt xi
i i d/dt i i 0 i xi
xi yi zi d/dt * + * * + * * + * 0 * d/dt j d/dt xi d/dt xi d/dt xi
yi d/dt yi yi d/dt yi yi d/dt yi
j j d/dt j j 0 j yi
i j k d/dt * + * * + * * + * 0 * d/dt k i i i
zi d/dt zi zi d/dt zi zi d/dt zi
k k d/dt k k 0 k zi
ai d/dt vi d/dt d/dt d/dt d/dt d/dt + d/dt + d/dt + d/dt + d/dt + + d/dt d/dt d/dt + + + + + + + + + + + + + * * *
ri + * * * d/dt * + * * + * * + * 0 * d/dt i * d/dt i * d/dt j * d/dt k * d/dt i * d/dt j * d/dt k * d^2/dt^2 i * d^2/dt^2 j * d^2/dt^2 k * d^2/dt^2 i * d^2/dt^2 j * d^2/dt^2 k d^2/dt^2 xi d^2/dt^2 yi d^2/dt^2 zi
xi d/dt xi xi d/dt xi xi d/dt xi
i i d/dt i i 0 i xi
xi yi zi d/dt * + * * + * * + * 0 * d/dt j d/dt xi d/dt yi d/dt zi xi yi zi xi yi zi
yi d/dt yi yi d/dt yi yi d/dt yi
j j d/dt j j 0 j yi xi yi zi * d/dt d/dt * d/dt d/dt * d/dt d/dt * d/dt 0 * d/dt 0 * d/dt 0 0 0 0 i j k
i j k d/dt * + * * + * * + * 0 * d/dt k
zi d/dt zi zi d/dt zi zi d/dt zi xi i yi j zi k xi yi zi
k k d/dt k k 0 k zi
Fi * * * * * * * * * * * * * * +
mi mi mi mi mi mi mi mi mi mi mi mi mi mi * mi d^2/dt^2 i
ai d/dt vi d/dt d/dt d/dt d/dt d/dt + d/dt + d/dt + d/dt + d/dt + + d/dt d/dt d/dt + + + + + + + + + + + + + * * *
ri + * * * d/dt * + * * + * * + * 0 * d/dt i * d/dt i * d/dt j * d/dt k * d/dt i * d/dt j * d/dt k * d^2/dt^2 i * d^2/dt^2 j * d^2/dt^2 k * d^2/dt^2 i * d^2/dt^2 j * d^2/dt^2 k d^2/dt^2 xi d^2/dt^2 yi d^2/dt^2 zi xi
xi d/dt xi xi d/dt xi xi d/dt xi * mi d^2/dt^2 j
i i d/dt i i 0 i xi
xi yi zi d/dt * + * * + * * + * 0 * d/dt j d/dt xi d/dt yi d/dt zi xi yi zi xi yi zi yi
yi d/dt yi yi d/dt yi yi d/dt yi
j j d/dt j j 0 j yi xi yi zi * d/dt d/dt * d/dt d/dt * d/dt d/dt * d/dt 0 * d/dt 0 * d/dt 0 0 0 0 i j k * mi d^2/dt^2 k
i j k d/dt * + * * + * * + * 0 * d/dt k
zi d/dt zi zi d/dt zi zi d/dt zi xi i yi j zi k xi yi zi zi
k k d/dt k k 0 k zi
rc x x +
sum(i=1,n) * sum(i=1,n) * * sum(i=1,n) / i
mi mi * mi xi sum mi
ri + * * * * sum(i=1,n) / j
xi yi zi * mi yi sum mi
i j k * sum(i=1,n) / k
/ sum(i=1,n) / sum(i=1,n) * mi zi sum mi
mi mi
vc d/dt rc
pc * *
sum mi sum mi
vc d/dt rc
ac d/dt d/dt
vc d/dt rc
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