Multiplicative and Affine Poisson Structures on Lie Groups

... Affine Poisson structures are more general then multiplicative ones, but they also have very simple properties. For example, it is already known to Dazord and Sondaz that their symplectic leaves are orbits of the “dressing actions”. We show that the dressing actions are Poisson actions; their Poisso ...

... Affine Poisson structures are more general then multiplicative ones, but they also have very simple properties. For example, it is already known to Dazord and Sondaz that their symplectic leaves are orbits of the “dressing actions”. We show that the dressing actions are Poisson actions; their Poisso ...

Lecture 8. Quaternions

... Overview, motivation Background Definition and properties Rotation using unit quaternions Intuition Using quaternions to represent rotations Why we love quaternions. ...

... Overview, motivation Background Definition and properties Rotation using unit quaternions Intuition Using quaternions to represent rotations Why we love quaternions. ...

Drinfel`d-Ihara relations for p-adic multi

... multi-zeta values. In §7, we prove the Drinfel’d-Ihara relations. The proofs of the 2-cycle and 3cycle relations are fairly straightforward. In §7.3, we prove the 5-cycle relation, by first expressing the frobenius invariant path in terms of Coleman integrals and then taking a limit which enables us ...

... multi-zeta values. In §7, we prove the Drinfel’d-Ihara relations. The proofs of the 2-cycle and 3cycle relations are fairly straightforward. In §7.3, we prove the 5-cycle relation, by first expressing the frobenius invariant path in terms of Coleman integrals and then taking a limit which enables us ...

8.5 Collisions 8 Momentum

... External forces may have an effect after the collision: • Billiard balls encounter friction with the table and the air. • After a collision of two trucks, the combined wreck slides along the pavement and friction decreases its momentum. • Two space vehicles docking in orbit have the same net momentu ...

... External forces may have an effect after the collision: • Billiard balls encounter friction with the table and the air. • After a collision of two trucks, the combined wreck slides along the pavement and friction decreases its momentum. • Two space vehicles docking in orbit have the same net momentu ...

input

... pertains only to GBASIS=STO, N21, N31, or N311. NDFUNC = number of heavy atom polarization functions to be used. These are usually d functions, except for MINI/MIDI. The term "heavy" means Na on up when GBASIS=STO, HW, or N21, and from Li on up otherwise. The value may not exceed 3. The variable POL ...

... pertains only to GBASIS=STO, N21, N31, or N311. NDFUNC = number of heavy atom polarization functions to be used. These are usually d functions, except for MINI/MIDI. The term "heavy" means Na on up when GBASIS=STO, HW, or N21, and from Li on up otherwise. The value may not exceed 3. The variable POL ...

Momentum is conserved for all collisions as long as external forces

... glider. The loaded glider is initially at rest. The unloaded glider collides with the loaded glider and the two gliders stick together. Describe the motion of the gliders after the collision. Answer: The mass of the stuck-together gliders is four times that of the unloaded glider. The velocity of th ...

... glider. The loaded glider is initially at rest. The unloaded glider collides with the loaded glider and the two gliders stick together. Describe the motion of the gliders after the collision. Answer: The mass of the stuck-together gliders is four times that of the unloaded glider. The velocity of th ...