# DOLLS and SLLOD Algorithm

1. Jun 9, 2013

### Tilde90

Apparently, this is the DOLLS tensor Hamiltonian:

[ tex ] H = H_0 + \sum q_i p_i : ∇u(t)^T [ /tex ]

These are the derived equations of motion:

[ tex ] \dot{q}_i = p_i/m + q_i \cdot ∇u [ /tex ]

[ tex ] \dot{p}_i = F_i - ∇u \cdot p_i [ /tex ]

And these are the SLLOD equations of motion:

[ tex ] \dot{q}_i = p_i/m + q_i \cdot ∇u [ /tex ]

[ tex ] \dot{p}_i = F_i - p_i \cdot ∇u [ /tex ]

For me this is nonsense. What is a division of an outer product (I guess), [ tex ] \sum q_i p_i [ /tex ], by a transposed vector? And, most of all, what is the difference between the equations of motion of these two methods?

Last edited: Jun 9, 2013