Pretty much what the title says. What is the purpose of the TSR-2's anhedral wingtips? I've heard someone say that they use it to counter yawing I think but is this the true reason or is it something else?
In the document "TSR2 with Hindsight", a lengthy documentation of TSR2 development by the Royal Air Force Historical Society, the reason given for the wingtip anhedral is the correction of lateral and longitudinal stability. Being a high-wing design, the anhedral was used to lower the sideslip-induced rolling moment.
To quote from TSR2 with hindsight:
At re-freeze, the wing was moved, its planform changed slightly and the tips given anhedral to reconcile lateral and longitudinal stability requirements; a very complex joint rib resulted. The wing already had a centre-line joint but only after great resistance from the weight-saving auditors.
The re-freeze in turn was the result of supersonic wind tunnel testing in 1960:
It was not until March 1960 that supersonic wind-tunnel test results were again available and one effect of the resultant design re-freeze was further refinement of the rear fuselage lines.
Turning down wingtips had been employed before in a high-wing design where re-designing the complete wing had been out of the question: The Heinkel 162. Here, the name for that modification was "Lippisch-Ohren" (Lippisch ears) after the person who had proposed them first for his delta-winged designs.