  We theoretically study static and dynamic properties of short Josephson
junctions (JJ) with singlet and triplet Josephson coupling. In singlet
Josephson weak links, two singlet superconductors S are connected with each
other by a normal film (N) or wire. Triplet JJs, which we denote
S$_{\text{m}}$/N(F)/S$_{\text{m}}$, are formed by two singlet BCS
superconductors covered by a thin layer of a weak ferromagnet F$_{\text{w}}$.
These superconductors S$_{\text{m}}$ are separated from the N (or F) layer by
spin filters, which pass electrons with only one spin orientation. The triplet
Cooper pairs propagating from the left (right) superconductors S$_{\text{m}}$
differ from each other not only by polarizations, but also by chiralities. The
latter is determined by the magnetization orientation in weak ferromagnets
F$_{\text{w}}$. We obtain analytical formulas for the critical Josephson
current in both types of the JJs. If chiralities of the triplet Cooper pairs
penetrating into the N film in S$_{\text{m}}$/N(F)/S$_{\text{m}}$ JJs from the
left and right S$_{\text{m}}$ are different, the Josephson current is not zero
in the absence of the phase difference (spontaneous Josephson current). We also
calculate the admittance $Y(\Omega)$ for arbitrary frequencies $\Omega$ in the
case of singlet JJs and for low frequencies in the case of triplet JJs. At low
temperatures $T$, the real part of the admittance $Y^{\prime}(\Omega)$ in
singlet JJs starts to increase from zero at ${\hbar \Omega \geq
\Delta_{\text{sg}}}$, but at ${T \geq \Delta_{\text{sg}}}$, it has a peak at
low frequencies the magnitude of which is determined by inelastic processes.
The subgap $\Delta_{\text{sg}}$ depends on transparencies of the S/N interfaces
and on the phase difference $2 \chi_{0}$. The low-frequency peak in
$Y^{\prime}(\Omega)$ in triplet JJs disappears.
