Universal Reference Frame
Alejandro A. Torassa
Creative Commons Attribution 3.0 License
(2013) Buenos Aires, Argentina
atorassa@gmail.com
Abstract
In classical mechanics, this paper presents the universal reference frame.

Universal Reference Frame
The universal reference frame is a reference frame fixed to the center of mass of the
universe.
The position r˚ a , the velocity v˚ a , and the acceleration a˚ a of a particle A of mass ma relative
˚ are given by:
to the universal reference frame S,
r˚ a =

RR

(Fa /ma ) dt dt

R

v˚ a = (Fa /ma ) dt
a˚ a = (Fa /ma )
where Fa is the net force acting on particle A.
From the above equations the following equations are obtained:
ma r˚ a −

RR

Fa dt dt = 0

→

2
1/2 m r
a ˚a

− 1/2 ma (

↓
→

↓

%

ma a˚ a − Fa = 0

→

where 1/2 v˚ a2 =

R

(Fa /ma ) dt dt)2 = 0

↓

ma v˚ a − Fa dt = 0

R

RR

a˚ a d r˚ a → 1/2 ma v˚ a2 =

2
1/2 m v
a ˚a

R

− Fa d r˚ a = 0
↓

2
1/2 m a
a ˚a

R

− 1/2 ma (Fa /ma )2 = 0

ma a˚ a d r˚ a → 1/2 ma v˚ a2 =
1

R

Fa d r˚ a