Muzzle velocity design. In a side by side comparison with the .50 BMG, the titanium round "of any caliber" released almost 28 times the energy of the .50 BMG, with only a 27% mean loss in momentum. Energy, in most cases, is what is lethal to the target, not momentum. In conventional guns, muzzle velocity is determined by the quantity of the propellant (burn speed, expansion), the mass of the projectile, and the length of the barrel. A slower-burning propellant needs a longer barrel to burn completely, but can, on the other hand, use a heavier projectile. A faster-burning propellant may accelerate
Angular velocity which shows a connection with the Lie group of rotations. We prove that angular velocity tensor is skew symmetric, i.e. formula_63 satisfies formula_64. A rotation matrix "A" is orthogonal, inverse to its transpose, so we have formula_65. For formula_66 a frame matrix, taking the time derivative of the equation gives: Applying the formula formula_68, Thus, "W" is the negative of its transpose, which implies it is skew symmetric. At any instant formula_70, the angular velocity tensor represents a linear map between the position vector formula_71 and the velocity vectors formula_72 of a point on a rigid body rotating around the