t

r

r

s

x

y

z

Chất ñiểmQuỹ ñạo

Vị trí r(t)

Vị trí r(t+∆t)

Hệ quy chiếu

ðộ dịch chuyển ∆r

( ) ( )trttrr��� −∆+=∆

t

x

y

z

r(t)

r(t+∆t)

∆r

tb

rv

t

∆=∆

�

�

s

t

∆=∆

vtb

t

v

dt

rd

t

rv

t

��

� =∆∆

=→∆

�

dt

dzv

dt

dyv

dt

dxv zyx ===

t

x

y

zr(t)

r(t+∆t)

v(t)

v(t+∆t)

v(t+∆t)

∆v

tb

va

t

∆=∆

�

�

dt

vd

t

va

t

��

� =∆∆

=→∆

�dt

dva

dt

dva

dt

dva z

z

y

yx

x ===

a

a

at

an

utunR

ut

� � �� �� � � � � � �� � � � ��� � �� � � � � � � � � �� ��

un

� � �� �� � � � � � �� � � � � �

R

� � � � �� � � � � �� � � �� �

atan

a

�n t n t

v dva a a u u

R dt= + = +� � � � �

g,

v � � � � � � �� �� � � � θ

� � �� � � �

v0

g

θ

x y

t t

dt

vdg

�

� = x

y

g

dt

dvg

dt

dv yx =−=

yyxx vgtvconstvv �� +−===⇒

∫∫∫ −==tv

vy

v

vx dtgdvdv

y

y

x

x

t

t

θθ vvvv yx ==

gtvvvv yx −== θθ

gtvdt

dyvv

dt

dxv yx −==== θθ

( )∫∫∫∫ −==tytx

dtgtvdydtvdx θθ

t

( )���� x

v

gxy

−=

θθ

( ) ( )

����� gttvytvx −== θθ

==⇒=dt

dvaconstv t�

n n n

va a u u

R= =� � �

v

a

R

K’

V

K

t

r r’

K K’

R K’

Kx

y

z

r’

Rr

x’

y’

z’

K

K’

K’ K

r r R′= +�

� �

v v V′= +�

� �

x

y

z

x’

y’

z’

v’

V

v

dtRddtrddtrd�

�� +=

K

K’ K’ K

K’

a a A′= +�

� �

aa�� =