- #1
Tilde90
- 22
- 0
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?
[ 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?
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