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I´m working on statistical mechanics, so I´m not so familiar with some things on the course.

I must solve the follwing problem for homework:

show that every galilean transformation g on the (galilean space, using natural galilean structure) space RxR^3 (first R linked to time, R^3 linked to 3 spatial coordinates) can be written in a unique way as the composition of a uniform motion g_1, a translation g_2, and a rotation g_3:

g = g_1 . g_2 . g_3

(thus the dimension of the galilean group is 3 + 4 + 3 = 10)

it is easy to show that g_1, g_2 and g_3 are galilean transformation. but I don´t know how to show that

they can ¨represent¨ any galilean transformation g. and less I can show uniqueness of it.

best regards

rayo