如果位於 的一隻小海龜，在無窮小的時距 中，若無外力作用會依此方向 持續前進，這就是牛頓之『慣性定律』，可以描述為 turtle.forward( ) 。假使此刻同時受到外力 作用，將向外力 方向偏移，可以看成是 turtle.right(   ) 或 turtle.left(   ) ，此處 ，可滿足牛頓的『第二運動定律』 。

如是一隻『圓周運動』之小海龜︰

Figure 2: The velocity vectors at time t and time t + dt are moved from the orbit on the left to new positions where their tails coincide, on the right. Because the velocity is fixed in magnitude at v = r ω, the velocity vectors also sweep out a circular path at angular rate ω. As dt → 0, the acceleration vector a becomes perpendicular to v, which means it points toward the center of the orbit in the circle on the left. Angle ω dt is the very small angle between the two velocities and tends to zero as dt→ 0.

 

自可表達成︰

pi@raspberrypi:~ $ python3
Python 3.4.2 (default, Oct 19 2014, 13:31:11) 
[GCC 4.9.1] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import turtle
>>> turtle.setup(width=800, height=600)
>>> turtle.shape('turtle')
>>> turtle.mode('logo')
>>> 
>>> def 圓周運動():
...     for 重複 in range(360):
...         turtle.forward(1)
...         turtle.right(1)
... 
>>> 圓周運動()
>>>

 

 

難到這小海龜的『軌跡』能夠違背

Galilean invariance

Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames. Galileo Galilei first described this principle in 1632 in his Dialogue Concerning the Two Chief World Systems using the example of a ship travelling at constant velocity, without rocking, on a smooth sea; any observer doing experiments below the deck would not be able to tell whether the ship was moving or stationary.

 

？不符合

Galilean transformation

In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. These transformations together with spatial rotations and translations in space and time form the inhomogeneous Galilean group (assumed throughout below). Without the translations in space and time the group is the homogeneous Galilean group. The Galilean group is the group of motions of Galilean relativity action on the four dimensions of space and time, forming the Galilean geometry. This is the passive transformation point of view. The equations below, although apparently obvious, are valid only at speeds much less than the speed of light. In special relativity the Galilean transformations are replaced by Poincaré transformations; conversely, the group contraction in the classical limit c → ∞ of Poincaré transformations yields Galilean transformations.

Galileo formulated these concepts in his description of uniform motion.^[1] The topic was motivated by his description of the motion of a ball rolling down a ramp, by which he measured the numerical value for the acceleration of gravity near the surface of the Earth.

……

Galilean transformations

The Galilean symmetries can be uniquely written as the composition of a rotation, a translation and a uniform motion of spacetime.^[6] Let x represent a point in three-dimensional space, and t a point in one-dimensional time. A general point in spacetime is given by an ordered pair (x, t).

A uniform motion, with velocity v, is given by

 

where v ∈ ℝ³. A translation is given by

where a ∈ ℝ³ and s ∈ ℝ. A rotation is given by

 

where G : ℝ³ → ℝ³ is an orthogonal transformation.^[6]

As a Lie group, the Galilean transformations span 10 dimensions,^[6] i.e., comprise 10 generators.

 

的嘛！