用戶:CaffeineP/數學式的推導(表格形式)

另見用戶:CaffeineP/質點力學。

																													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