Classical mechanics on noncommutative space with Lie-algebraic structure

► Suggest a useful method to look for new Lie-algebraic noncommutative spaces. ► Find out two new Lie-algebraic noncommutative spaces. ► Derive Newton and Hamilton equations that present unimaginable extra forces. ► Analyse the source of unimaginable extra forces from space noncummutativity. ► Provide various intriguing classical trajectories.