We revise the solution to the problem of Hamiltonization of the $n$-dimensional Veselova non-holonomic system studied previously in [1]. Namely, we give a short and direct proof of the hamiltonization theorem and also show the trajectorial equivalence of the problem with the geodesic flow on the ellipsoid.	
	
		
		
	
	
	
	
																		
						Keywords:						
												
						nonholonomic systems, integrability, geodesic flows						
						
						
												
						
							
						
						
		
Citation:
	
	Fedorov Y. N., Jovanović B., Hamiltonization of the generalized Veselova LR system, Regular and Chaotic Dynamics,	
	2009, Volume 14, Numbers 4-5,
	 pp. 495-505