Graceli variational periodic function from the periodic function .
E (t + 2kπ ) = E ( t)

An important property of the function E ( t ) is the frequency .
We say that a function is periodic with period T , when f ( t + T) = f ( t ) for all t .
As the length of S1 is 2π , when t > 2π or t < - 2π to describe an arc of length t , from the point ( 1,0) , we need to take more than one turn over S1 .

In particular, where k is an integer , the final ends of the arc length T = 2kπ always coincide with the point ( 1,0) . This implies that , whatever the actual number teo integer k , we
E (t + 2kπ ) = E ( t)
and therefore e ( t) is periodic function of period 2π . Of course, any other integer multiple of 2π is also a time for this function .

Graceli variational periodic function from the periodic function .
E (t + 2kπ ) = E ( t)

For a system with curved ball and holes in the structure.
E (t + 2kπ ) = E ( t). [v p = d ]
Change course and distance traveled in the periphery of a sphere . Taking into account variations in the structure of the sphere.
For a system of differential sides , as the example of the dog that runs toward the owner, while he also runs another distant parallel .
E (t + 2kπ ) = E ( t). [ a / d = â ]
Acceleration = distance divided by â

For a system change and acceleration.
E (t + 2kπ ) = E ( t). [v . the TC / ] [+]

For a system in rotation and oscillation pulses .
E (t + 2kπ ) = E ( t). [ R . the . p / [ c / t ] .
Rotation , oscillation and wrists .

For a general system with all these variables .

E (t + 2kπ ) = E ( t). [ p = v d] [ +] E (t + 2kπ ) = E ( t). [ a / d = â ] [ + ] E ( t + 2kπ ) = E ( t ) . [v . the TC / ] [+] E (t + 2kπ ) = E ( t). [ R . the . p / [ c / t ] .

for an infinitesimal system variables.
E (t + 2kπ ) = E ( t). [ p = v d] [/ ] E (t + 2kπ ) = E ( t). [ a / d = â ] [ / ] E ( t + 2kπ ) = E ( t ) . [v . the TC / ] [/ ] E (t + 2kπ ) = E ( t). [ R . the . p / [ c / t ] .