Lagrangian of the Einstein's special relativity with universal parameter c
(SRc​) is invariant under Poincar\'e transformation which preserves
Lorentz metric ημν​. The SRc​ has been extended to be
one which is invariant under de Sitter transformation that preserves so called
Beltrami metric Bμν​. There are two universal parameters c and R in
this Special Relativity (denote it as SRcR​). The
Lagrangian-Hamiltonian formulism of SRcR​ is formulated in this
paper. The canonic energy, canonic momenta, and 10 Noether charges
corresponding to the space-time's de Sitter symmetry are derived. The canonical
quantization of the mechanics for SRcR​-free particle is
performed. The physics related to it is discussed.Comment: 24 pages, no figur